// Numbas version: exam_results_page_options {"name": "Ecuaci\u00f3n Radical reducible a Cuadr\u00e1tica ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "name": "Ecuaci\u00f3n Radical reducible a Cuadr\u00e1tica ", "advice": "

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\\begin{align}
\\simplify[std]{x-{a/2}}&=\\sqrt{\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}} \\\\\\\\
\\left(\\simplify[std]{x-{a/2}}\\right)^2&=\\left(\\sqrt{\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}}\\right)^2
\\end{align}

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Desarrollando y ordenando:

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\\begin{align}
\\simplify[std]{x^2-{a}x+{(a/2)^2}}&=\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}\\\\\\\\
\\simplify[std]{x^2-{a+b}x+{a*b}}&=\\simplify[std]{0}
\\end{align}

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Factoricemos y resolvamos:

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\\begin{align}
(\\simplify{(x-{a})})(\\simplify{x-{b}})=&\\simplify{0}
\\end{align}

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\$\\simplify{(x-{a}={0})} \\,\\,\\,\\,;\\,\\,\\, \\simplify{(x-{b}={0})} \$

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\$\\simplify{x_1={a}} \\,\\,\\,\\,;\\,\\,\\, \\simplify{(x_2={b})}\$

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Verificando las soluciones encontradas $\\,\\,\\simplify{x_1={a}}\\,\\,\\,$ y $\\,\\,\\,\\simplify{x_2={b}}\\,\\,$ en la ecuación inicial, nos quedamos con $\\simplify{x_2={b}}$, ya que ella la satisface.

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La solución de la ecuación es:

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\$\\simplify{(x_2={b})}\$

", "variables": {"b": {"definition": "random(2..9 except -a)", "group": "Ungrouped variables", "name": "b", "templateType": "anything", "description": ""}, "a": {"definition": "random(-9..-2)", "group": "Ungrouped variables", "name": "a", "templateType": "anything", "description": ""}}, "ungrouped_variables": ["a", "b"], "extensions": [], "parts": [{"scripts": {}, "type": "gapfill", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacements": [], "type": "jme", "showFeedbackIcon": true, "checkvariablenames": false, "expectedvariablenames": [], "vsetrangepoints": 5, "notallowed": {"showStrings": false, "strings": ["."], "partialCredit": 0, "message": "

"}, "answer": "{b}", "showCorrectAnswer": true, "marks": 1, "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "showpreview": true, "scripts": {}, "answersimplification": "Std", "vsetrange": [0, 1], "checkingaccuracy": 0.001}], "variableReplacements": [], "showCorrectAnswer": true, "prompt": "

Ingrese su respuesta como un número entero o bien una fracción.

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$x=$ [[0]]

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", "marks": 0}], "functions": {}, "tags": [], "preamble": {"css": "", "js": ""}, "statement": "

Resolver el siguiente ecuación:

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\$\\begin{eqnarray*}\\simplify[std]{x-{a/2}}&=&\\sqrt{\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}}\\end{eqnarray*}\$

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", "rulesets": {"std": ["All", "fractionnumbers"]}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Shows how to define variables to stop degenerate examples.

"}, "variable_groups": [{"name": "Unnamed group", "variables": []}], "type": "question", "contributors": [{"name": "Patricio Ramirez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/191/"}]}]}], "contributors": [{"name": "Patricio Ramirez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/191/"}]}