// Numbas version: exam_results_page_options
{"name": "Ecuaci\u00f3n  Radical reducible a Cuadr\u00e1tica .jk", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Shows how to define variables to stop degenerate examples.</p>"}, "ungrouped_variables": ["a", "b"], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Ecuaci\u00f3n  Radical reducible a Cuadr\u00e1tica .jk", "variables": {"b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9 except -a)", "description": "", "name": "b"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..-2)", "description": "", "name": "a"}}, "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>", "parts": [{"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, "gaps": [{"answer": "{b}", "checkingtype": "absdiff", "vsetrange": [0, 1], "variableReplacements": [], "expectedvariablenames": [], "notallowed": {"message": "<p>Input your answer as a fraction and not a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "showpreview": true, "marks": 1, "vsetrangepoints": 5, "showFeedbackIcon": true, "scripts": {}, "answersimplification": "Std", "type": "jme", "showCorrectAnswer": true}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true}], "tags": [], "functions": {}, "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>", "preamble": {"css": "", "js": ""}, "extensions": [], "variable_groups": [{"variables": [], "name": "Unnamed group"}], "rulesets": {"std": ["All", "fractionnumbers"]}, "type": "question", "contributors": [{"name": "Jos Klenner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/84/"}]}]}], "contributors": [{"name": "Jos Klenner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/84/"}]}