{"id":13041,"date":"2026-03-24T05:00:30","date_gmt":"2026-03-24T09:00:30","guid":{"rendered":"https:\/\/wp.glbgpt.com\/?p=13041"},"modified":"2026-07-28T23:31:33","modified_gmt":"2026-07-29T03:31:33","slug":"best-ai-math-solver-tested","status":"publish","type":"post","link":"https:\/\/wp.glbgpt.com\/es\/hub\/best-ai-math-solver-tested","title":{"rendered":"Mejor AI Math Solver (2026): Herramientas probadas para obtener resultados precisos"},"content":{"rendered":"<style>.math-test-grid{display:grid;grid-template-columns:repeat(auto-fit,minmax(min(100%,320px),1fr));gap:16px;align-items:start;margin:18px 0 16px}.math-test-card{box-sizing:border-box;min-width:0;overflow:hidden}.model-output-details{margin-top:8px}.model-output-details summary{display:block;cursor:pointer;overflow-wrap:anywhere;border:1px solid #52709a;background:#eef4fb;color:#173b63;border-radius:7px;padding:11px 13px;font-weight:700;min-height:22px}.model-output-details summary::-webkit-details-marker{display:none}.model-output-details summary:focus-visible{outline:3px solid #2457d6;outline-offset:3px}.model-output-details .output-hide{display:none}.model-output-details[open] .output-show{display:none}.model-output-details[open] .output-hide{display:inline}.model-output-details pre{white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto}@media(max-width:680px){.math-test-grid{grid-template-columns:1fr}.math-test-card{padding:14px!important}.model-output-details summary{padding:12px!important}}<\/style>\n\n\n\n<div class=\"glb-test-update\" style=\"border:1px solid #b9d7c4;background:#effaf3;border-radius:8px;padding:16px 18px;margin:0 0 18px\"><strong>Fresh test, July 28, 2026:<\/strong> We ran the same five-problem math test through GPT-5.6 Sol, Claude Opus 5, and Gemini 3.6 Flash using one OpenAI-compatible API workflow. All three solved all five questions correctly and verified their answers. The meaningful differences in this small test were response style and single-run latency\u2014not correctness.<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Respuesta r\u00e1pida:<\/strong> There was no accuracy winner in our current test. GPT-5.6 Sol, Claude Opus 5, and Gemini 3.6 Flash each scored 5\/5. Gemini 3.6 Flash returned first at 17.45 seconds, Claude Opus 5 followed at 17.89 seconds, and GPT-5.6 Sol took 32.85 seconds. Those times come from one API request per model, so they should not be treated as a universal speed benchmark.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The best AI math solver is the one that gets the answer right, shows a method you can audit, follows the requested format, and checks for hidden conditions. That is why our test included ordinary algebra, a geometry word problem, multi-step percentages, an extraneous-root trap, and calculus\u2014not just easy final-answer questions.<\/p>\n\n\n\n<nav class=\"glb-article-toc\" aria-label=\"\u00cdndice\" style=\"border:1px solid #f3d18b;background:#fff8e6;border-radius:8px;padding:18px;margin:18px 0\"><strong>\u00cdndice<\/strong><ul><li><a href=\"#how-we-tested\">C\u00f3mo realizamos las pruebas<\/a><\/li><li><a href=\"#results\">Results at a glance<\/a><\/li><li><a href=\"#five-tests\">Five math tests<\/a><\/li><li><a href=\"#choose\">Which solver should you choose?<\/a><\/li><li><a href=\"#globalgpt-math-solver\">Use GlobalGPT Math Solver<\/a><\/li><li><a href=\"#better-results\">How to get better results<\/a><\/li><li><a href=\"#faq\">PREGUNTAS FRECUENTES<\/a><\/li><\/ul><\/nav>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"how-we-tested\">How We Tested the Best AI Math Solvers<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">We tested the newest relevant models available through the same approved API connection: GPT-5.6 Sol, Claude Opus 5, and Gemini 3.6 Flash. The current model names were checked against the available API catalog and the providers\u2019 current pages for <a href=\"https:\/\/openai.com\/index\/introducing-gpt-5-6\/\" target=\"_blank\" rel=\"noreferrer noopener\">GPT-5.6<\/a>, <a href=\"https:\/\/www.anthropic.com\/news\/claude-opus-5\" target=\"_blank\" rel=\"noreferrer noopener\">Claude Opus 5<\/a>, y <a href=\"https:\/\/blog.google\/innovation-and-ai\/models-and-research\/gemini-models\/\" target=\"_blank\" rel=\"noreferrer noopener\">Gemini 3,6 Flash<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each model received the same system instruction and the same five questions in one request. We did not supply a temperature or model-specific sampling setting. Every answer had to include steps, a final answer, and verification. No web search or external math tool was requested.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Score area<\/th><th>What we checked<\/th><th>Peso<\/th><\/tr><\/thead><tbody><tr><td>Correctness<\/td><td>Correct final result on all five questions<\/td><td>50%<\/td><\/tr><tr><td>Step quality<\/td><td>Auditable method with the important transformations shown<\/td><td>20%<\/td><\/tr><tr><td>Instrucciones a seguir<\/td><td>Requested labels and complete coverage of every task<\/td><td>15%<\/td><\/tr><tr><td>Verificaci\u00f3n<\/td><td>Back-substitution, condition checks, or differentiation<\/td><td>15%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Five questions are enough to expose obvious weaknesses, but not enough to prove that one model is best across every branch of mathematics. For a wider student-tool comparison, see the <a href=\"https:\/\/www.glbgpt.com\/hub\/best-ai-for-homework\/\" target=\"_blank\" rel=\"noreferrer noopener\">best AI tools for homework<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"results\">Real API Test Results at a Glance<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Modelo<\/th><th>Correct answers<\/th><th>Correctness<\/th><th>Pasos<\/th><th>Instrucciones a seguir<\/th><th>Verificaci\u00f3n<\/th><th>Total<\/th><th>Single-run latency<\/th><\/tr><\/thead><tbody><tr><td>GPT-5.6 Sol<\/td><td>5\/5<\/td><td>50\/50<\/td><td>20\/20<\/td><td>15\/15<\/td><td>15\/15<\/td><td><strong>100\/100<\/strong><\/td><td>32.85 s<\/td><\/tr><tr><td>Claude Opus 5<\/td><td>5\/5<\/td><td>50\/50<\/td><td>20\/20<\/td><td>15\/15<\/td><td>15\/15<\/td><td><strong>100\/100<\/strong><\/td><td>17.89 s<\/td><\/tr><tr><td>Gemini 3,6 Flash<\/td><td>5\/5<\/td><td>50\/50<\/td><td>20\/20<\/td><td>15\/15<\/td><td>15\/15<\/td><td><strong>100\/100<\/strong><\/td><td>17.45 s<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Veredicto:<\/strong> all three models tied on mathematical correctness and verification in this test. Gemini 3.6 Flash was the fastest by a small margin over Claude Opus 5. GPT-5.6 Sol produced the most spacious, highly structured answer, but it was slower in this single run. Do not turn these three latency numbers into a general speed ranking without repeated tests.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you are deciding between an OpenAI model and alternatives, the <a href=\"https:\/\/www.glbgpt.com\/hub\/best-chatgpt-alternatives-for-math\/\" target=\"_blank\" rel=\"noreferrer noopener\">2026 ChatGPT alternatives for math comparison<\/a> covers the wider choice set.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"five-tests\">The Five Math Problems We Used<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Test 1: Algebra and Symmetric Expressions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Math ability:<\/strong> Algebra \u00b7 identity use \u00b7 equation recovery<\/p>\n\n\n\n<div class=\"math-test-grid\" style=\"display:grid;grid-template-columns:repeat(auto-fit,minmax(min(100%,320px),1fr));gap:16px;align-items:start;margin:18px 0 16px\"><article class=\"math-test-card\" data-test=\"Q1\" data-model=\"gpt-5.6-sol\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 1: Algebra and Symmetric Expressions<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> GPT-5.6 Sol \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Algebra \u00b7 identity use \u00b7 equation recovery<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q1 \u2014 Algebra: Real numbers x and y satisfy x + y = 11 and xy = 24. Find x^2 + y^2, then identify the unordered pair {x,y}.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">x&#178;+y&#178;=73; {x,y}={3,8}. Must use the given sum\/product consistently and verify both values.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models used the symmetric-identity shortcut, recovered 3 and 8 from the quadratic, and verified the sum, product, and target value.<\/p><p><strong>Response time:<\/strong> 32.85 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">### Steps\n\nGiven\n\\[\nx+y=11,\\qquad xy=24.\n\\]\n\nUse\n\\[\nx^2+y^2=(x+y)^2-2xy.\n\\]\n\nThus\n\\[\nx^2+y^2=11^2-2(24)=121-48=73.\n\\]\n\nTo identify \\(x\\) and \\(y\\), they must be the roots of\n\\[\nt^2-(x+y)t+xy=0,\n\\]\nso\n\\[\nt^2-11t+24=0.\n\\]\n\nFactoring:\n\\[\n(t-3)(t-8)=0.\n\\]\n\nHence the two values are \\(3\\) and \\(8\\).\n\n### Final answer\n\n\\[\n\\boxed{x^2+y^2=73},\\qquad \\boxed{\\{x,y\\}=\\{3,8\\}}.\n\\]\n\n### Verification\n\n\\[\n3+8=11,\\qquad 3\\cdot 8=24,\n\\]\nand\n\\[\n3^2+8^2=9+64=73.\n\\]<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q1\" data-model=\"claude-opus-5\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 1: Algebra and Symmetric Expressions<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Claude Opus 5 \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Algebra \u00b7 identity use \u00b7 equation recovery<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q1 \u2014 Algebra: Real numbers x and y satisfy x + y = 11 and xy = 24. Find x^2 + y^2, then identify the unordered pair {x,y}.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">x&#178;+y&#178;=73; {x,y}={3,8}. Must use the given sum\/product consistently and verify both values.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models used the symmetric-identity shortcut, recovered 3 and 8 from the quadratic, and verified the sum, product, and target value.<\/p><p><strong>Response time:<\/strong> 17.89 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps\n- (x+y)&#178; = x&#178; + 2xy + y&#178;, so x&#178; + y&#178; = 11&#178; \ufffd?? 2(24) = 121 \ufffd?? 48 = 73.\n- x and y are roots of t&#178; \ufffd?? 11t + 24 = 0 = (t \ufffd?? 3)(t \ufffd?? 8).\n\nFinal answer\nx&#178; + y&#178; = 73; {x, y} = {3, 8}.\n\nVerification\n3 + 8 = 11 \ufffd??, 3&#183;8 = 24 \ufffd??, 9 + 64 = 73 \ufffd??. Discriminant 121 \ufffd?? 96 = 25 &gt; 0, so both roots are real.<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q1\" data-model=\"gemini-3.6-flash\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 1: Algebra and Symmetric Expressions<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Gemini 3.6 Flash \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Algebra \u00b7 identity use \u00b7 equation recovery<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q1 \u2014 Algebra: Real numbers x and y satisfy x + y = 11 and xy = 24. Find x^2 + y^2, then identify the unordered pair {x,y}.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">x&#178;+y&#178;=73; {x,y}={3,8}. Must use the given sum\/product consistently and verify both values.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models used the symmetric-identity shortcut, recovered 3 and 8 from the quadratic, and verified the sum, product, and target value.<\/p><p><strong>Response time:<\/strong> 17.45 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps:\n1. Use the algebraic identity $x^2 + y^2 = (x + y)^2 - 2xy$.\n2. Substitute the given values $x + y = 11$ and $xy = 24$:\n   $$x^2 + y^2 = 11^2 - 2(24) = 121 - 48 = 73$$\n3. To find $x$ and $y$, construct the quadratic equation whose roots are $x$ and $y$:\n   $$t^2 - (x+y)t + xy = 0 \\implies t^2 - 11t + 24 = 0$$\n4. Factor the quadratic equation:\n   $$(t - 3)(t - 8) = 0 \\implies t = 3 \\text{ or } t = 8$$\n\nFinal answer:\n$x^2 + y^2 = 73$; Unordered pair $\\{x, y\\} = \\{3, 8\\}$.\n\nVerification:\n$3 + 8 = 11$, $3 \\times 8 = 24$, and $3^2 + 8^2 = 9 + 64 = 73$.<\/pre><\/details><\/article>\n<\/div>\n\n\n\n<p class=\"test-group-summary wp-block-paragraph\"><strong>Group takeaway:<\/strong> All three models used the symmetric-identity shortcut, recovered 3 and 8 from the quadratic, and verified the sum, product, and target value.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Test 2: Geometry Word Problem<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Math ability:<\/strong> Geometry \u00b7 equation setup \u00b7 uniqueness<\/p>\n\n\n\n<div class=\"math-test-grid\" style=\"display:grid;grid-template-columns:repeat(auto-fit,minmax(min(100%,320px),1fr));gap:16px;align-items:start;margin:18px 0 16px\"><article class=\"math-test-card\" data-test=\"Q2\" data-model=\"gpt-5.6-sol\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 2: Geometry Word Problem<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> GPT-5.6 Sol \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Geometry \u00b7 equation setup \u00b7 uniqueness<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q2 \u2014 Geometry\/word problem: A rectangle has perimeter 34 cm and diagonal 13 cm. Find its side lengths and area. Explain why the dimensions are determined.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">Sides 5 cm and 12 cm; area 60 cm&#178;. Must connect perimeter and diagonal conditions and explain uniqueness up to side order.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models formed a+b=17 and a\u00b2+b\u00b2=169, derived ab=60, found 5 and 12, and checked the perimeter and diagonal.<\/p><p><strong>Response time:<\/strong> 32.85 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">### Steps\n\nLet the positive side lengths be \\(a\\) and \\(b\\).\n\nThe perimeter is \\(34\\) cm:\n\\[\n2(a+b)=34,\n\\]\nso\n\\[\na+b=17.\n\\]\n\nThe diagonal is \\(13\\) cm, so by the Pythagorean theorem,\n\\[\na^2+b^2=13^2=169.\n\\]\n\nUsing\n\\[\n(a+b)^2=a^2+b^2+2ab,\n\\]\nwe obtain\n\\[\n17^2=169+2ab.\n\\]\n\nTherefore,\n\\[\n289=169+2ab,\n\\]\n\\[\n2ab=120,\n\\]\n\\[\nab=60.\n\\]\n\nThe side lengths are roots of\n\\[\nt^2-17t+60=0.\n\\]\n\nFactoring:\n\\[\n(t-5)(t-12)=0.\n\\]\n\nThus the side lengths are \\(5\\) cm and \\(12\\) cm. The area is\n\\[\nA=ab=60\\text{ cm}^2.\n\\]\n\nThe dimensions are determined because their sum and product are fixed. The quadratic has exactly the two positive roots \\(5\\) and \\(12\\), which give the same rectangle up to interchanging length and width.\n\n### Final answer\n\n\\[\n\\boxed{\\text{Side lengths: }5\\text{ cm and }12\\text{ cm}}\n\\]\n\\[\n\\boxed{\\text{Area: }60\\text{ cm}^2}\n\\]\n\n### Verification\n\nPerimeter:\n\\[\n2(5+12)=2(17)=34\\text{ cm}.\n\\]\n\nDiagonal:\n\\[\n\\sqrt{5^2+12^2}=\\sqrt{25+144}=\\sqrt{169}=13\\text{ cm}.\n\\]\n\nArea:\n\\[\n5\\cdot 12=60\\text{ cm}^2.\n\\]<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q2\" data-model=\"claude-opus-5\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 2: Geometry Word Problem<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Claude Opus 5 \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Geometry \u00b7 equation setup \u00b7 uniqueness<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q2 \u2014 Geometry\/word problem: A rectangle has perimeter 34 cm and diagonal 13 cm. Find its side lengths and area. Explain why the dimensions are determined.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">Sides 5 cm and 12 cm; area 60 cm&#178;. Must connect perimeter and diagonal conditions and explain uniqueness up to side order.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models formed a+b=17 and a\u00b2+b\u00b2=169, derived ab=60, found 5 and 12, and checked the perimeter and diagonal.<\/p><p><strong>Response time:<\/strong> 17.89 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps\n- Let sides be a, b &gt; 0. Perimeter: 2(a+b) = 34 \ufffd?? a + b = 17.\n- Diagonal (Pythagoras): a&#178; + b&#178; = 169.\n- 2ab = (a+b)&#178; \ufffd?? (a&#178;+b&#178;) = 289 \ufffd?? 169 = 120 \ufffd?? ab = 60.\n- a, b are roots of t&#178; \ufffd?? 17t + 60 = 0 = (t \ufffd?? 5)(t \ufffd?? 12).\n\nFinal answer\nSides 5 cm and 12 cm; area 60 cm&#178;.\n\nVerification\n2(5+12) = 34 \ufffd??, 5&#178; + 12&#178; = 25 + 144 = 169 = 13&#178; \ufffd??, area = 60 \ufffd??.\nWhy determined: the two conditions fix the sum and product of the side lengths, and a monic quadratic is uniquely determined by its sum and product of roots. Discriminant 289 \ufffd?? 240 = 49 &gt; 0 gives two positive roots, which are the same rectangle up to relabeling a and b \ufffd?? so the dimensions are unique as an unordered pair.<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q2\" data-model=\"gemini-3.6-flash\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 2: Geometry Word Problem<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Gemini 3.6 Flash \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Geometry \u00b7 equation setup \u00b7 uniqueness<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q2 \u2014 Geometry\/word problem: A rectangle has perimeter 34 cm and diagonal 13 cm. Find its side lengths and area. Explain why the dimensions are determined.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">Sides 5 cm and 12 cm; area 60 cm&#178;. Must connect perimeter and diagonal conditions and explain uniqueness up to side order.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models formed a+b=17 and a\u00b2+b\u00b2=169, derived ab=60, found 5 and 12, and checked the perimeter and diagonal.<\/p><p><strong>Response time:<\/strong> 17.45 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps:\n1. Let the side lengths be $a &gt; 0$ and $b &gt; 0$.\n2. The perimeter equation is $2(a + b) = 34 \\implies a + b = 17$.\n3. By the Pythagorean theorem, the diagonal gives $a^2 + b^2 = 13^2 = 169$.\n4. Use $(a + b)^2 = a^2 + b^2 + 2ab$:\n   $$17^2 = 169 + 2ab \\implies 289 = 169 + 2ab \\implies 2ab = 120 \\implies ab = 60$$\n5. The area is $A = ab = 60\\text{ cm}^2$.\n6. Side lengths $a$ and $b$ are the positive roots of $t^2 - 17t + 60 = 0$:\n   $$(t - 5)(t - 12) = 0 \\implies t = 5 \\text{ or } t = 12$$\n7. **Why dimensions are determined:** The perimeter and diagonal uniquely fix both the sum $(a+b = 17)$ and product $(ab = 60)$ of the positive side lengths. A system specifying the sum and product of two numbers uniquely defines the set of roots of a quadratic polynomial, giving a unique pair of side lengths up to order.\n\nFinal answer:\nSide lengths: $5\\text{ cm}$ and $12\\text{ cm}$; Area: $60\\text{ cm}^2$. The dimensions are determined because perimeter and diagonal uniquely fix the sum and product of the adjacent side lengths, leading to a unique positive quadratic solution set.\n\nVerification:\nPerimeter: $2(5 + 12) = 34\\text{ cm}$. Diagonal: $\\sqrt{5^2 + 12^2} = \\sqrt{25 + 144} = \\sqrt{169} = 13\\text{ cm}$. Area: $5 \\times 12 = 60\\text{ cm}^2$.<\/pre><\/details><\/article>\n<\/div>\n\n\n\n<p class=\"test-group-summary wp-block-paragraph\"><strong>Group takeaway:<\/strong> All three models formed a+b=17 and a\u00b2+b\u00b2=169, derived ab=60, found 5 and 12, and checked the perimeter and diagonal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Test 3: Multi-Step Percentage Reasoning<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Math ability:<\/strong> Arithmetic \u00b7 sequential percentages \u00b7 verification<\/p>\n\n\n\n<div class=\"math-test-grid\" style=\"display:grid;grid-template-columns:repeat(auto-fit,minmax(min(100%,320px),1fr));gap:16px;align-items:start;margin:18px 0 16px\"><article class=\"math-test-card\" data-test=\"Q3\" data-model=\"gpt-5.6-sol\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 3: Multi-Step Percentage Reasoning<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> GPT-5.6 Sol \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Arithmetic \u00b7 sequential percentages \u00b7 verification<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q3 \u2014 Multi-step reasoning: A store marks an item up by 25% from its cost, then gives a 20% discount on the marked price. The customer pays $120 before tax. Find the original cost and the net percentage change from cost to the paid price.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">Original cost $120; net change 0%. Must multiply 1.25&#215;0.80 rather than subtract percentage points.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models correctly recognized that the sequential multipliers cancel and verified the $120 \u2192 $150 \u2192 $120 path.<\/p><p><strong>Response time:<\/strong> 32.85 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">### Steps\n\nLet the original cost be \\(C\\).\n\nA \\(25\\%\\) markup multiplies the cost by\n\\[\n1+0.25=1.25.\n\\]\n\nThe marked price is therefore\n\\[\n1.25C.\n\\]\n\nA \\(20\\%\\) discount means the customer pays \\(80\\%\\) of the marked price:\n\\[\n0.80(1.25C)=120.\n\\]\n\nSince\n\\[\n0.80\\cdot 1.25=1,\n\\]\nthe equation becomes\n\\[\nC=120.\n\\]\n\nThe paid price equals the original cost, so the net percentage change is\n\\[\n\\frac{120-120}{120}\\cdot 100\\%=0\\%.\n\\]\n\n### Final answer\n\n\\[\n\\boxed{\\text{Original cost}=\\$120}\n\\]\n\\[\n\\boxed{\\text{Net percentage change}=0\\%}\n\\]\n\n### Verification\n\nA \\(25\\%\\) markup on \\(\\$120\\) gives\n\\[\n120(1.25)=\\$150.\n\\]\n\nA \\(20\\%\\) discount on \\(\\$150\\) gives\n\\[\n150(0.80)=\\$120.\n\\]\n\nThus the paid price is exactly equal to the original cost.<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q3\" data-model=\"claude-opus-5\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 3: Multi-Step Percentage Reasoning<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Claude Opus 5 \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Arithmetic \u00b7 sequential percentages \u00b7 verification<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q3 \u2014 Multi-step reasoning: A store marks an item up by 25% from its cost, then gives a 20% discount on the marked price. The customer pays $120 before tax. Find the original cost and the net percentage change from cost to the paid price.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">Original cost $120; net change 0%. Must multiply 1.25&#215;0.80 rather than subtract percentage points.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models correctly recognized that the sequential multipliers cancel and verified the $120 \u2192 $150 \u2192 $120 path.<\/p><p><strong>Response time:<\/strong> 17.89 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps\n- Let cost = C. Marked price = 1.25C.\n- Sale price = 0.80 \ufffd? 1.25C = 1.00C.\n- Paid price = 120 \ufffd?? C = 120.\n- Net change = (120 \ufffd?? 120)\/120 = 0.\n\nFinal answer\nOriginal cost = $120; net change from cost to paid price = 0% (no change).\n\nVerification\n120 \ufffd?? marked up 25% \ufffd?? 150 \ufffd?? 20% off \ufffd?? 150 \ufffd?? 30 = 120 \ufffd??. Note the multipliers: 1.25 \ufffd? 0.80 = 1 exactly, so the markup and discount cancel regardless of cost. (Result is before tax, as stated.)<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q3\" data-model=\"gemini-3.6-flash\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 3: Multi-Step Percentage Reasoning<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Gemini 3.6 Flash \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Arithmetic \u00b7 sequential percentages \u00b7 verification<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q3 \u2014 Multi-step reasoning: A store marks an item up by 25% from its cost, then gives a 20% discount on the marked price. The customer pays $120 before tax. Find the original cost and the net percentage change from cost to the paid price.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">Original cost $120; net change 0%. Must multiply 1.25&#215;0.80 rather than subtract percentage points.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models correctly recognized that the sequential multipliers cancel and verified the $120 \u2192 $150 \u2192 $120 path.<\/p><p><strong>Response time:<\/strong> 17.45 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps:\n1. Let $C &gt; 0$ be the original cost in dollars.\n2. Markup of 25%: Marked price $M = C \\times (1 + 0.25) = 1.25C$.\n3. Discount of 20% on marked price: Paid price $P = M \\times (1 - 0.20) = 1.25C \\times 0.80 = 1.00C$.\n4. Set $P = \\$120$:\n   $$1.00C = 120 \\implies C = \\$120$$\n5. Net percentage change from cost to paid price:\n   $$\\text{Net Change \\%} = \\frac{P - C}{C} \\times 100\\% = \\frac{120 - 120}{120} \\times 100\\% = 0\\%$$\n\nFinal answer:\nOriginal cost: $\\$120$; Net percentage change: $0\\%$.\n\nVerification:\nMarkup: $\\$120 \\times 1.25 = \\$150$. Discount: $\\$150 \\times 0.80 = \\$120$. Paid price matches $\\$120$, and cost equals paid price ($0\\%$ net change).<\/pre><\/details><\/article>\n<\/div>\n\n\n\n<p class=\"test-group-summary wp-block-paragraph\"><strong>Group takeaway:<\/strong> All three models correctly recognized that the sequential multipliers cancel and verified the $120 \u2192 $150 \u2192 $120 path.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Test 4: Extraneous-Root Verification Trap<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Math ability:<\/strong> Conditions \u00b7 candidate checking \u00b7 logical validity<\/p>\n\n\n\n<div class=\"math-test-grid\" style=\"display:grid;grid-template-columns:repeat(auto-fit,minmax(min(100%,320px),1fr));gap:16px;align-items:start;margin:18px 0 16px\"><article class=\"math-test-card\" data-test=\"Q4\" data-model=\"gpt-5.6-sol\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 4: Extraneous-Root Verification Trap<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> GPT-5.6 Sol \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Conditions \u00b7 candidate checking \u00b7 logical validity<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q4 \u2014 Verification trap: Solve sqrt(x + 6) = x over the real numbers. Check every candidate in the original equation and explain why any rejected candidate fails.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">x=3 only. Must identify x\u22650, test x=3 and x=\u22122 in the original equation, and reject \u22122 as extraneous.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models stated the nonnegative restriction, checked both candidates, and rejected \u22122 in the original equation. This supports the reliability conclusion.<\/p><p><strong>Response time:<\/strong> 32.85 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">### Steps\n\nSolve\n\\[\n\\sqrt{x+6}=x\n\\]\nover the real numbers.\n\nBecause a square root is nonnegative, the right-hand side must satisfy\n\\[\nx\\ge 0.\n\\]\nAlso, the radicand requires \\(x+6\\ge 0\\), which is automatically satisfied when \\(x\\ge 0\\).\n\nSquare both sides:\n\\[\nx+6=x^2.\n\\]\n\nRearrange:\n\\[\nx^2-x-6=0.\n\\]\n\nFactor:\n\\[\n(x-3)(x+2)=0.\n\\]\n\nThe candidates are\n\\[\nx=3\\quad\\text{or}\\quad x=-2.\n\\]\n\nBoth candidates must be checked in the original equation because squaring can introduce extraneous solutions.\n\nFor \\(x=3\\):\n\\[\n\\sqrt{3+6}=\\sqrt9=3,\n\\]\nso \\(x=3\\) is valid.\n\nFor \\(x=-2\\):\n\\[\n\\sqrt{-2+6}=\\sqrt4=2\\ne -2,\n\\]\nso \\(x=-2\\) is invalid. It fails because the principal square root is always nonnegative, while the proposed right-hand side is negative.\n\n### Final answer\n\n\\[\n\\boxed{x=3}\n\\]\n\n### Verification\n\nSubstitution into the original equation gives\n\\[\n\\sqrt{3+6}=3,\n\\]\n\\[\n3=3.\n\\]\n\nThe rejected candidate \\(x=-2\\) gives \\(2=-2\\), which is false.<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q4\" data-model=\"claude-opus-5\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 4: Extraneous-Root Verification Trap<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Claude Opus 5 \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Conditions \u00b7 candidate checking \u00b7 logical validity<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q4 \u2014 Verification trap: Solve sqrt(x + 6) = x over the real numbers. Check every candidate in the original equation and explain why any rejected candidate fails.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">x=3 only. Must identify x\u22650, test x=3 and x=\u22122 in the original equation, and reject \u22122 as extraneous.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models stated the nonnegative restriction, checked both candidates, and rejected \u22122 in the original equation. This supports the reliability conclusion.<\/p><p><strong>Response time:<\/strong> 17.89 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps\n- Domain\/conditions: need x + 6 \ufffd?\ufffd 0 (x \ufffd?\ufffd \ufffd??6) and, since the principal square root is nonnegative, x \ufffd?\ufffd 0.\n- Square both sides: x + 6 = x&#178; \ufffd?? x&#178; \ufffd?? x \ufffd?? 6 = 0 \ufffd?? (x \ufffd?? 3)(x + 2) = 0 \ufffd?? x = 3 or x = \ufffd??2.\n- Test in the original equation: x = 3 \ufffd?? \ufffd??9 = 3 \ufffd??. x = \ufffd??2 \ufffd?? \ufffd??4 = 2 \ufffd?\ufffd \ufffd??2 \ufffd??.\n\nFinal answer\nx = 3.\n\nVerification\n\ufffd??(3 + 6) = \ufffd??9 = 3 = x \ufffd??.\nWhy \ufffd??2 fails: squaring is not reversible \ufffd?? it turns \ufffd??(x+6) = x into an equation also satisfied by \ufffd??(x+6) = \ufffd??x. x = \ufffd??2 satisfies that second branch, but it violates the condition x \ufffd?\ufffd 0 because the principal root cannot be negative. It is an extraneous root introduced by squaring.<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q4\" data-model=\"gemini-3.6-flash\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 4: Extraneous-Root Verification Trap<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Gemini 3.6 Flash \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Conditions \u00b7 candidate checking \u00b7 logical validity<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q4 \u2014 Verification trap: Solve sqrt(x + 6) = x over the real numbers. Check every candidate in the original equation and explain why any rejected candidate fails.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">x=3 only. Must identify x\u22650, test x=3 and x=\u22122 in the original equation, and reject \u22122 as extraneous.<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models stated the nonnegative restriction, checked both candidates, and rejected \u22122 in the original equation. This supports the reliability conclusion.<\/p><p><strong>Response time:<\/strong> 17.45 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps:\n1. Equation: $\\sqrt{x + 6} = x$.\n2. Domain\/Condition Restrictions:\n   - Radicand non-negative: $x + 6 \\ge 0 \\implies x \\ge -6$.\n   - Principal square root non-negative: $\\sqrt{x + 6} \\ge 0 \\implies x \\ge 0$.\n   - Combined domain restriction: $x \\ge 0$.\n3. Square both sides:\n   $$x + 6 = x^2 \\implies x^2 - x - 6 = 0$$\n4. Factor:\n   $$(x - 3)(x + 2) = 0 \\implies \\text{Candidates: } x = 3, x = -2$$\n5. Check candidates in original equation $\\sqrt{x + 6} = x$:\n   - For $x = 3$: $\\sqrt{3 + 6} = \\sqrt{9} = 3$. Valid (LHS = RHS).\n   - For $x = -2$: $\\sqrt{-2 + 6} = \\sqrt{4} = 2 \\neq -2$. Rejected.\n6. **Reason for rejection:** The principal real square root function $\\sqrt{\\cdot}$ always yields a non-negative real value ($\\sqrt{4} = +2$). Since the right side is $-2$, the equation $2 = -2$ is false. $x = -2$ is an extraneous solution introduced by squaring.\n\nFinal answer:\n$x = 3$.\n\nVerification:\nLHS at $x = 3$: $\\sqrt{3 + 6} = \\sqrt{9} = 3 = \\text{RHS}$.\nLHS at $x = -2$: $\\sqrt{-2 + 6} = \\sqrt{4} = 2 \\neq -2 = \\text{RHS}$.<\/pre><\/details><\/article>\n<\/div>\n\n\n\n<p class=\"test-group-summary wp-block-paragraph\"><strong>Group takeaway:<\/strong> All three models stated the nonnegative restriction, checked both candidates, and rejected \u22122 in the original equation. This supports the reliability conclusion.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Test 5: Calculus with Differentiation Check<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Math ability:<\/strong> Calculus \u00b7 substitution \u00b7 reverse verification<\/p>\n\n\n\n<div class=\"math-test-grid\" style=\"display:grid;grid-template-columns:repeat(auto-fit,minmax(min(100%,320px),1fr));gap:16px;align-items:start;margin:18px 0 16px\"><article class=\"math-test-card\" data-test=\"Q5\" data-model=\"gpt-5.6-sol\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 5: Calculus with Differentiation Check<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> GPT-5.6 Sol \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Calculus \u00b7 substitution \u00b7 reverse verification<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q5 \u2014 Calculus: Evaluate the indefinite integral \u222b 2x*e^(x^2) dx. Name the substitution and verify by differentiation.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">e^(x&#178;)+C using u=x&#178;. Must differentiate the result back to 2x&#183;e^(x&#178;).<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models named u=x\u00b2, integrated e^u, restored x\u00b2, and differentiated the result back to the original integrand.<\/p><p><strong>Response time:<\/strong> 32.85 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">### Steps\n\nEvaluate\n\\[\n\\int 2x e^{x^2}\\,dx.\n\\]\n\nUse \\(u\\)-substitution:\n\\[\nu=x^2.\n\\]\n\nThen\n\\[\ndu=2x\\,dx.\n\\]\n\nTherefore,\n\\[\n\\int 2x e^{x^2}\\,dx=\\int e^u\\,du.\n\\]\n\nIntegrating:\n\\[\n\\int e^u\\,du=e^u+C.\n\\]\n\nSubstitute \\(u=x^2\\):\n\\[\ne^{x^2}+C.\n\\]\n\nThis antiderivative is valid for all real \\(x\\).\n\n### Final answer\n\n\\[\n\\boxed{\\int 2x e^{x^2}\\,dx=e^{x^2}+C}\n\\]\n\n### Verification\n\nDifferentiate the result using the chain rule:\n\\[\n\\frac{d}{dx}\\left(e^{x^2}+C\\right)\n=e^{x^2}\\cdot 2x\n=2x e^{x^2}.\n\\]\n\nThis matches the original integrand.<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q5\" data-model=\"claude-opus-5\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 5: Calculus with Differentiation Check<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Claude Opus 5 \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Calculus \u00b7 substitution \u00b7 reverse verification<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q5 \u2014 Calculus: Evaluate the indefinite integral \u222b 2x*e^(x^2) dx. Name the substitution and verify by differentiation.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">e^(x&#178;)+C using u=x&#178;. Must differentiate the result back to 2x&#183;e^(x&#178;).<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models named u=x\u00b2, integrated e^u, restored x\u00b2, and differentiated the result back to the original integrand.<\/p><p><strong>Response time:<\/strong> 17.89 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps\n- Substitution: u = x&#178;, du = 2x dx.\n- \ufffd?\ufffd 2x e^(x&#178;) dx = \ufffd?\ufffd e^u du = e^u + C = e^(x&#178;) + C.\n\nFinal answer\ne^(x&#178;) + C.\n\nVerification\nd\/dx [e^(x&#178;) + C] = e^(x&#178;) &#183; d\/dx(x&#178;) = 2x e^(x&#178;) \ufffd?? (chain rule). Valid for all real x; the integrand is continuous on \ufffd?\ufffd.<\/pre><\/details><\/article>\n<article class=\"math-test-card\" data-test=\"Q5\" data-model=\"gemini-3.6-flash\" style=\"border:1px solid #ccd7e2;border-top:5px solid #208052;border-radius:10px;background:#fff;min-width:0;overflow:hidden;padding:16px\"><div style=\"display:flex;justify-content:space-between;gap:10px;align-items:flex-start;flex-wrap:wrap\"><div><strong style=\"font-size:1.05em\">Test 5: Calculus with Differentiation Check<\/strong><div style=\"font-size:.9em;color:#536273\"><strong>Modelo:<\/strong> Gemini 3.6 Flash \u00b7 <strong>Test date:<\/strong> July 28, 2026<\/div><\/div><span aria-label=\"Result: Pass\" style=\"display:inline-block;background:#e8f7ee;color:#12633b;border:1px solid #8fc9a7;border-radius:999px;padding:4px 9px;font-weight:700\">PASS \u00b7 20\/20<\/span><\/div><p style=\"font-size:.9em;color:#536273\"><strong>Math ability:<\/strong> Calculus \u00b7 substitution \u00b7 reverse verification<\/p><h4 style=\"margin:16px 0 6px\">Entrada<\/h4><p style=\"overflow-wrap:anywhere\">Q5 \u2014 Calculus: Evaluate the indefinite integral \u222b 2x*e^(x^2) dx. Name the substitution and verify by differentiation.<\/p><h4 style=\"margin:14px 0 6px\">Expected answer \/ scoring key<\/h4><p style=\"overflow-wrap:anywhere\">e^(x&#178;)+C using u=x&#178;. Must differentiate the result back to 2x&#183;e^(x&#178;).<\/p><h4 style=\"margin:14px 0 6px\">Result and score<\/h4><p><strong>Pass \u00b7 20\/20<\/strong><\/p><ul><li>Correctness: 10\/10<\/li><li>Step quality: 4\/4<\/li><li>Instruction following: 3\/3<\/li><li>Verification\/conditions: 3\/3<\/li><\/ul><p><strong>Lo que pas\u00f3:<\/strong> All three models named u=x\u00b2, integrated e^u, restored x\u00b2, and differentiated the result back to the original integrand.<\/p><p><strong>Response time:<\/strong> 17.45 seconds for the full five-question request.<\/p><p style=\"margin:14px 0 7px\"><strong>Real model output:<\/strong> Full response for this test item, not an edited excerpt.<\/p><details class=\"model-output-details\"><summary aria-label=\"Toggle full model output\"><span class=\"output-show\">\u25b6 Show full model output<\/span><span class=\"output-hide\">\u2212 Hide model output<\/span><\/summary><pre style=\"white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;max-width:100%;overflow-x:auto;background:#f6f8fb;border:1px solid #e1e6ed;border-radius:7px;padding:12px;font:13px\/1.5 ui-monospace,SFMono-Regular,Consolas,monospace\">Steps:\n1. Evaluate $\\int 2x e^{x^2} \\, dx$ over domain $x \\in (-\\infty, \\infty)$.\n2. Name of substitution: $u$-substitution with $u = x^2$.\n3. Compute differential: $du = 2x \\, dx$.\n4. Substitute into integral:\n   $$\\int 2x e^{x^2} \\, dx = \\int e^u \\, du = e^u + C$$\n5. Back-substitute $u = x^2$:\n   $$e^{x^2} + C$$\n\nFinal answer:\n$e^{x^2} + C$  (Substitution: $u = x^2$)\n\nVerification:\nDifferentiate the result with respect to $x$ using the chain rule:\n$$\\frac{d}{dx}\\left(e^{x^2} + C\\right) = e^{x^2} \\cdot \\frac{d}{dx}(x^2) + 0 = 2x e^{x^2}$$\nThis recovers the original integrand.<\/pre><\/details><\/article>\n<\/div>\n\n\n\n<p class=\"test-group-summary wp-block-paragraph\"><strong>Group takeaway:<\/strong> All three models named u=x\u00b2, integrated e^u, restored x\u00b2, and differentiated the result back to the original integrand.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The cards show why method checks matter even when every final answer is correct. The companion review of <a href=\"https:\/\/www.glbgpt.com\/hub\/can-chatgpt-do-math\/\" target=\"_blank\" rel=\"noreferrer noopener\">what ChatGPT gets right and wrong in math<\/a> explains where answer-only evaluation can miss a weak process.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The extraneous-root test is one example of a broader failure pattern. See <a href=\"https:\/\/www.glbgpt.com\/hub\/why-is-chatgpt-so-bad-at-math\/\" target=\"_blank\" rel=\"noreferrer noopener\">why ChatGPT can fail at math<\/a> for more cases where conditions and verification change the result.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"choose\">Which AI Math Solver Should You Choose?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Choose GPT-5.6 Sol for highly structured worked solutions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">GPT-5.6 Sol gave the longest and most explicitly segmented answer in this run. It is a good fit when you want every transformation, condition, and verification written out. It was the slowest of the three in this single request, so speed-sensitive users should test it on their own workload.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Choose Claude Opus 5 for concise but rigorous explanations<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Claude Opus 5 reached every correct answer with compact reasoning and strong condition checks. Its API response was close to Gemini\u2019s latency in this run. A capture-encoding artifact affected a few mathematical symbols in the saved raw response; the underlying steps and answers remained clear and correct.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Choose Gemini 3.6 Flash for fast, complete responses<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Gemini 3.6 Flash was the fastest model in this one-run comparison and still included all required verification. That makes it a practical first choice for quick checks, but the 0.44-second lead over Claude is too small to treat as a permanent speed advantage.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For an OpenAI-specific decision, see <a href=\"https:\/\/www.glbgpt.com\/hub\/which-chatgpt-model-is-best-for-math\/\" target=\"_blank\" rel=\"noreferrer noopener\">which ChatGPT model is best for math<\/a>. For study workflows, the <a href=\"https:\/\/www.glbgpt.com\/hub\/how-to-use-chatgpt-for-homework\/\" target=\"_blank\" rel=\"noreferrer noopener\">ChatGPT homework workflow<\/a> shows how to ask for explanations instead of answer-only output.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"globalgpt-math-solver\">A Simpler Way to Solve and Check Math in GlobalGPT<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If you want a focused interface instead of building API requests, the <a href=\"https:\/\/www.glbgpt.com\/features\/ai-math-solver\" target=\"_blank\" rel=\"noreferrer noopener\">Resolutor matem\u00e1tico con IA GlobalGPT<\/a> lets you type a problem or upload an image and request a step-by-step explanation in one place. Use it to get a worked solution, then ask for a verification step before relying on the answer.<\/p>\n\n\n\n<div class=\"glb-math-cta\" style=\"border:1px solid #f0c45a;background:#fff8e6;border-radius:10px;padding:18px;margin:22px 0;text-align:center\"><strong>Try the GlobalGPT AI Math Solver<\/strong><p>Enter or upload a math problem, review the steps, and ask the solver to check the result.<\/p><p><a href=\"https:\/\/www.glbgpt.com\/features\/ai-math-solver\" target=\"_blank\" rel=\"noreferrer noopener\" style=\"display:inline-block;background:#fec33a;color:#17202a;text-decoration:none;border-radius:7px;padding:11px 18px;font-weight:700\">Open AI Math Solver<\/a><\/p><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"better-results\">How to Get Better Results from Any AI Math Solver<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Obtener los mejores resultados de un solucionador matem\u00e1tico de IA depende de c\u00f3mo se formule la pregunta. Una indicaci\u00f3n clara puede marcar la diferencia entre una respuesta d\u00e9bil y una soluci\u00f3n \u00fatil paso a paso.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Para resolver:<\/strong> \u201cSolve this step by step and explain each transformation.\u201d<\/li><li><strong>Para comprobar el trabajo:<\/strong> \u201cFind my first incorrect step and explain why it fails.\u201d<\/li><li><strong>For conditions:<\/strong> \u201cState the domain and test every candidate in the original equation.\u201d<\/li><li><strong>For calculus:<\/strong> \u201cName the substitution and verify the antiderivative by differentiation.\u201d<\/li><li><strong>Para los problemas de palabras:<\/strong> \u201cDefine variables and write the equations before solving.\u201d<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Before trusting a difficult answer, compare the final result with the assumptions and verification\u2014not just another model\u2019s final number. The <a href=\"https:\/\/www.glbgpt.com\/hub\/is-chatgpt-good-at-math\/\" target=\"_blank\" rel=\"noreferrer noopener\">accuracy review of ChatGPT for math<\/a> offers more practical checking criteria.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"faq\">Preguntas frecuentes<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">What is the best AI math solver in this test?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">GPT-5.6 Sol, Claude Opus 5, and Gemini 3.6 Flash tied at 5\/5 on the July 28, 2026 test. Gemini returned fastest in the single run, but the sample is too small to declare a universal accuracy or speed winner.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Which model was fastest?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Gemini 3.6 Flash returned in 17.45 seconds, Claude Opus 5 in 17.89 seconds, and GPT-5.6 Sol in 32.85 seconds. These are one-run API measurements, not long-term latency benchmarks.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u00bfPuede la IA resolver problemas de palabras con precisi\u00f3n?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes, but ask the model to define variables, form equations, and verify the result. All three tested models solved the geometry and percentage word problems correctly in this test.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Can an AI math solver keep an invalid answer?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. Squaring equations and dividing by variable expressions can introduce or hide invalid cases. Ask the solver to state conditions and test every candidate in the original problem.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u00bfPuede la IA leer problemas matem\u00e1ticos escritos a mano?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Multimodal math tools can accept image input, but handwriting recognition was not tested through the text-only API run described here. The GlobalGPT Math Solver page supports uploading a math-problem image for step-by-step help.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Can I use GlobalGPT for math problems?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. The GlobalGPT AI Math Solver provides a focused place to type or upload a problem and receive a step-by-step explanation. You should still review the conditions and request a verification step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Was this a paid, reproducible test?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The test used an authorized API connection on July 28, 2026 and consumed a reasonable amount of API usage. Each model received the same five questions and instructions in one request; no model-specific sampling settings were supplied.<\/p>\n\n\n\n<script type=\"application\/ld+json\">{\n    \"@context\": \"https:\\\/\\\/schema.org\",\n    \"@type\": \"FAQPage\",\n    \"mainEntity\": [\n        {\n            \"@type\": \"Question\",\n            \"name\": \"What is the best AI math solver in this test?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"GPT-5.6 Sol, Claude Opus 5, and Gemini 3.6 Flash tied at 5\\\/5 on the July 28, 2026 test. Gemini returned fastest in the single run, but the sample is too small to declare a universal accuracy or speed winner.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Which model was fastest?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"Gemini 3.6 Flash returned in 17.45 seconds, Claude Opus 5 in 17.89 seconds, and GPT-5.6 Sol in 32.85 seconds. These are one-run API measurements, not long-term latency benchmarks.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Can AI solve word problems accurately?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"Yes, but ask the model to define variables, form equations, and verify the result. All three tested models solved the geometry and percentage word problems correctly in this test.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Can an AI math solver keep an invalid answer?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"Yes. Squaring equations and dividing by variable expressions can introduce or hide invalid cases. Ask the solver to state conditions and test every candidate in the original problem.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Can AI read handwritten math problems?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"Multimodal math tools can accept image input, but handwriting recognition was not tested through the text-only API run described here. The GlobalGPT Math Solver page supports uploading a math-problem image for step-by-step help.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Can I use GlobalGPT for math problems?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"Yes. The GlobalGPT AI Math Solver provides a focused place to type or upload a problem and receive a step-by-step explanation. You should still review the conditions and request a verification step.\"\n            }\n        },\n        {\n            \"@type\": \"Question\",\n            \"name\": \"Was this a paid, reproducible test?\",\n            \"acceptedAnswer\": {\n                \"@type\": \"Answer\",\n                \"text\": \"The test used an authorized API connection on July 28, 2026 and consumed a reasonable amount of API usage. Each model received the same five questions and instructions in one request; no model-specific sampling settings were supplied.\"\n            }\n        }\n    ]\n}<\/script>","protected":false},"excerpt":{"rendered":"<p>Fresh test, July 28, 2026: We ran the same five-problem math test through GPT-5.6 Sol, Claude Opus 5, and Gemini 3.6 Flash using one OpenAI-compatible API workflow. All three solved all five questions correctly and verified their answers. The meaningful differences in this small test were response style and single-run latency\u2014not correctness. Quick answer: There [&hellip;]<\/p>","protected":false},"author":7,"featured_media":13093,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"Best AI Math Solver (2026): Tested Tools for Accurate Results","_seopress_titles_desc":"We tested GPT-5.6 Sol, Claude Opus 5, and Gemini 3.6 Flash on five math problems. Compare accuracy, steps, verification, and real API latency.","_seopress_robots_index":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-13041","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai-chat"],"_links":{"self":[{"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/posts\/13041","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/comments?post=13041"}],"version-history":[{"count":18,"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/posts\/13041\/revisions"}],"predecessor-version":[{"id":17341,"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/posts\/13041\/revisions\/17341"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/media\/13093"}],"wp:attachment":[{"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/media?parent=13041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/categories?post=13041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.glbgpt.com\/es\/wp-json\/wp\/v2\/tags?post=13041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}