// 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, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "name": "Ecuaci\u00f3n  Radical reducible a Cuadr\u00e1tica ", "advice": "<p>Elevemos ambos lados de la igualdad al cuadrado. No olvide que cuando se eleva al cuadrado, en ocasiones pueden aparecer soluciones extra&ntilde;as. Por eso es muy importante verificar que las soluciones encontradas satisfacen la ecuaci&oacute;n inicial.</p>\n<p>\\begin{align}<br/>\\simplify[std]{x-{a/2}}&amp;=\\sqrt{\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}} \\\\\\\\<br/>\\left(\\simplify[std]{x-{a/2}}\\right)^2&amp;=\\left(\\sqrt{\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}}\\right)^2<br/>\\end{align}</p>\n<p>Desarrollando y ordenando:</p>\n<p>\\begin{align}<br/>\\simplify[std]{x^2-{a}x+{(a/2)^2}}&amp;=\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}\\\\\\\\<br/>\\simplify[std]{x^2-{a+b}x+{a*b}}&amp;=\\simplify[std]{0}<br/>\\end{align}</p>\n<p>Factoricemos y resolvamos:</p>\n<p>\\begin{align}<br/>(\\simplify{(x-{a})})(\\simplify{x-{b}})=&amp;\\simplify{0}<br/>\\end{align}</p>\n<p>\\[\\simplify{(x-{a}={0})} \\,\\,\\,\\,;\\,\\,\\, \\simplify{(x-{b}={0})} \\]</p>\n<p>\\[\\simplify{x_1={a}} \\,\\,\\,\\,;\\,\\,\\, \\simplify{(x_2={b})}\\]</p>\n<p></p>\n<p>Verificando las soluciones encontradas $\\,\\,\\simplify{x_1={a}}\\,\\,\\,$ y $\\,\\,\\,\\simplify{x_2={b}}\\,\\,$ en la ecuaci&oacute;n inicial, nos quedamos con $\\simplify{x_2={b}}$, ya que ella la satisface.</p>\n<p>La soluci&oacute;n de la ecuaci&oacute;n es:</p>\n<p>\\[\\simplify{(x_2={b})}\\]</p>", "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": "<p>Input your answer as a fraction and not a decimal.</p>"}, "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": "<p>Ingrese su respuesta como un n&uacute;mero entero o bien una fracci&oacute;n.</p>\n<p>$x=$&nbsp;[[0]]&nbsp;</p>\n<p></p>\n<p></p>", "marks": 0}], "functions": {}, "tags": [], "preamble": {"css": "", "js": ""}, "statement": "<p>Resolver el siguiente ecuaci&oacute;n:</p>\n<p>\\[\\begin{eqnarray*}\\simplify[std]{x-{a/2}}&amp;=&amp;\\sqrt{\\simplify[std]{{b}x-{a*b}+{(a/2)^2}}}\\end{eqnarray*}\\]</p>\n<p></p>", "rulesets": {"std": ["All", "fractionnumbers"]}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Shows how to define variables to stop degenerate examples.</p>"}, "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/"}]}