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{"version":3,"file":"2N52-5-jfYFdGTA.js","sources":["../../src/exercices/2e/2N52-5.js"],"sourcesContent":["import { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { texFractionReduite } from '../../lib/outils/deprecatedFractions.js'\nimport { ecritureAlgebriqueSauf1, reduireAxPlusB, rienSi1 } from '../../lib/outils/ecritures'\nimport { sp } from '../../lib/outils/outilString.js'\nimport Exercice from '../deprecatedExercice.js'\nimport { context } from '../../modules/context.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nexport const dateDePublication = '02/05/2023'\nexport const titre = 'Solve equations with a quotient'\n\n/**\n * Mettre au même dénominateur des expressions littérales\n* @author Gilles Mora\n* 2N41-8\n*/\nexport const uuid = 'b5828'\nexport const ref = '2N52-5'\nexport default function ResoudreEquationsQuotient () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.nbCols = 1\n this.nbColsCorr = 1\n this.spacing = 1\n this.spacingCorr = 1\n this.nbQuestions = 2\n this.sup = 3\n this.nouvelleVersion = function () {\n this.sup = parseInt(this.sup)\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n let typesDeQuestionsDisponibles = []\n if (this.sup === 1) {\n typesDeQuestionsDisponibles = [1, 2]\n } else if (this.sup === 2) {\n typesDeQuestionsDisponibles = [3, 4]\n } else { typesDeQuestionsDisponibles = [1, 2, 3, 4] } // 1, 2, 3, 4, 5, 6, 7\n\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n for (let i = 0, texte, texteCorr, cpt = 0, typesDeQuestions, choix, consigne1, a, b, c, d, e, f, k1, k2; i < this.nbQuestions && cpt < 50;) {\n typesDeQuestions = listeTypeDeQuestions[i]\n consigne1 = 'Specify any prohibited values, then solve the equation:'\n switch (typesDeQuestions) {\n case 1:// (ax+b)/(cx+d)=0\n a = randint(-3, 9, 0)\n b = randint(-9, 9)\n c = randint(-9, 9, 0)\n d = randint(-9, 9)\n while (a * d - b * c === 0) {\n a = randint(-3, 9, 0)\n b = randint(-9, 9)\n c = randint(-9, 9, 0)\n d = randint(-9, 9)\n }\n choix = choice([true, false])\n texte = consigne1\n if (b === 0) {\n texte += `$\\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}}=0$. `\n } else {\n texte += `${choix ? `$\\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}}=0$` : `$\\\\dfrac{${b}${ecritureAlgebriqueSauf1(a)}x}{${reduireAxPlusB(c, d)}}=0$`}. `\n }\n if (context.isDiaporama) {\n texteCorr = ''\n } else {\n if (b === 0) {\n texteCorr = 'Determining the forbidden values amounts to determining the values which cancel the denominator of the quotient, since division by $0$ does not exist.<br>'\n } else {\n texteCorr = 'Determining the forbidden values amounts to determining the values which cancel the denominator of the quotient, since division by $0$ does not exist.<br>'\n }\n }\n texteCorr += `But $${reduireAxPlusB(c, d)}=0$ if and only if $x=${texFractionReduite(-d, c)}$. <br>So the set of forbidden values is $\\\\left\\\\{${texFractionReduite(-d, c)}\\\\right\\\\}$. <br>`\n if (b === 0) {\n texteCorr += `For all $x\\\\in \\\\mathbb{R}\\\\smallsetminus\\\\left\\\\{${texFractionReduite(-d, c)}\\\\right\\\\}$, <br>$\\\\begin{aligned}\\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}} &=0 \\\\\\\\${reduireAxPlusB(a, b)}&=0 ${sp(7)} \\\\text{ since }\\\\dfrac{A(x)}{B(x)}=0 \\\\text { if and only if } A(x)=0 \\\\text { and } B(x)\\\\neq 0\\\\\\\\x&= ${texFractionReduite(-b, a)}\\\\end{aligned}$<br>`\n } else {\n texteCorr += `For all $x\\\\in \\\\mathbb{R}\\\\smallsetminus\\\\left\\\\{${texFractionReduite(-d, c)}\\\\right\\\\}$,<br>$\\\\begin{aligned}${choix ? `\\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}}&=0` : `\\\\dfrac{${b}${ecritureAlgebriqueSauf1(a)}x}{${reduireAxPlusB(c, d)}}&=0`}\\\\\\\\${choix ? `${reduireAxPlusB(a, b)}&=0` : `${b}${ecritureAlgebriqueSauf1(a)}x&=0`}${sp(7)} \\\\text{ since }\\\\dfrac{A(x)}{B( x)}=0 \\\\text { if and only if } A(x)=0 \\\\text { and } B(x)\\\\neq 0\\\\\\\\x&= ${texFractionReduite(-b, a)}\\\\end{aligned}$<br>`\n }\n\n texteCorr += ` $${texFractionReduite(-b, a)}$ is not a forbidden value, so the solution set of this equation is $\\\\mathscr{S}=\\\\left\\\\{${texFractionReduite(-b, a)}\\\\right\\\\}$. `\n break\n case 2:// (ax^2+/-b)/(cx+d)=0\n a = randint(1, 4)\n k1 = randint(1, 10)\n b = a * k1 * k1\n c = randint(-9, 9, 0)\n k2 = randint(-4, 4, 0)\n d = c * k2\n\n choix = choice([true, false])\n texte = consigne1\n if (choice([true, false])) {\n texte += `${choix ? `$\\\\dfrac{${rienSi1(a)}x^2-${b}}{${reduireAxPlusB(c, d)}}=0$` : `$\\\\dfrac{${b}-${rienSi1(a)}x^2}{${reduireAxPlusB(c, d)}}=0$`}. `\n if (context.isDiaporama) {\n texteCorr = ''\n } else {\n texteCorr = 'Determining the forbidden values amounts to determining the values which cancel the denominator of the quotient, since division by $0$ does not exist.<br>'\n }\n texteCorr += `But $${reduireAxPlusB(c, d)}=0$ if and only if $x=${-k2}$. <br>So the set of forbidden values is $\\\\left\\\\{${-k2}\\\\right\\\\}$.<br>For all $x\\\\in \\\\mathbb{R}\\\\smallsetminus\\\\left\\\\{${-k2}\\\\right\\\\}$, <br>$\\\\begin{aligned}${choix ? `\\\\dfrac{${rienSi1(a)}x^2-${b}}{${reduireAxPlusB(c, d)}}&=0` : `\\\\dfrac{${b}-${rienSi1(a)}x^2}{${reduireAxPlusB(c, d)}}& =0`}\\\\\\\\${choix ? `${rienSi1(a)}x^2-${b}&=0` : `${b}-${rienSi1(a)}x^2&=0`}${sp(7)} \\\\text{ since }\\\\dfrac{A(x)}{B(x)}= 0 \\\\text { if and only if } A(x)=0 \\\\text { and } B(x)\\\\neq 0\\\\\\\\${rienSi1(a)}x^2&=${b}\\\\\\\\x^2&=${k1 * k1}\\\\\\\\x= ${k1}&\\\\text{ or } x= -${k1}\\\\end{aligned}$<br>`\n if (-k2 === k1 || k2 === k1) {\n if (-k2 === k1) {\n texteCorr += ` $${k1}$ is a forbidden value, so the solution set of this equation is $\\\\mathscr{S}=\\\\left\\\\{${-k1}\\\\right\\\\}$. `\n } else {\n texteCorr += ` $${-k1}$ is a forbidden value, so the solution set of this equation is $\\\\mathscr{S}=\\\\left\\\\{${k1}\\\\right\\\\}$. `\n }\n } else {\n texteCorr += ` $${-k1}$ and $${k1}$ are not forbidden values, so the solution set of this equation is $\\\\mathscr{S}=\\\\left\\\\{${-k1}\\\\,,\\\\,${k1}\\\\right\\\\}$. `\n }\n } else {\n texte += `${choix ? `$\\\\dfrac{${rienSi1(a)}x^2+${b}}{${reduireAxPlusB(c, d)}}=0$` : `$\\\\dfrac{${b}+${rienSi1(a)}x^2}{${reduireAxPlusB(c, d)}}=0$`}. `\n if (context.isDiaporama) {\n texteCorr = ''\n } else {\n texteCorr = 'Determining the forbidden values amounts to determining the values which cancel the denominator of the quotient, since division by $0$ does not exist.<br>'\n }\n texteCorr += `But $${reduireAxPlusB(c, d)}=0$ if and only if $x=${-k2}$. <br>So the set of forbidden values is $\\\\left\\\\{${-k2}\\\\right\\\\}$.<br>For all $x\\\\in \\\\mathbb{R}\\\\smallsetminus\\\\left\\\\{${-k2}\\\\right\\\\}$, <br>$\\\\begin{aligned}${choix ? `\\\\dfrac{${rienSi1(a)}x^2+${b}}{${reduireAxPlusB(c, d)}}&=0` : `\\\\dfrac{${b}+${rienSi1(a)}x^2}{${reduireAxPlusB(c, d)}}& =0`}\\\\\\\\${choix ? `${rienSi1(a)}x^2+${b}&=0` : `${b}+${rienSi1(a)}x^2&=0`}${sp(7)} \\\\text{ since }\\\\dfrac{A(x)}{B(x)}= 0 \\\\text { if and only if } A(x)=0 \\\\text { and } B(x)\\\\neq 0\\\\\\\\${rienSi1(a)}x^2&=-${b}\\\\\\\\x^2&=-${k1 * k1} \\\\end{aligned}$<br>`\n texteCorr += `Since $-${k1 * k1}<0$, this equation has no solution, so the solution set is $\\\\mathscr{S}=\\\\varnothing$. `\n }\n\n break\n case 3:// (ax+b)/(cx+d)=e\n a = randint(-3, 5, 0)\n b = randint(-9, 9)\n c = randint(-9, 9, 0)\n d = randint(-9, 9)\n e = randint(-9, 9, 0)\n while ((a * d - b * c === 0) || (a - e * c === 0)) {\n a = randint(-3, 5)\n b = randint(-9, 9)\n c = randint(-9, 9, 0)\n d = randint(-9, 9)\n e = randint(-9, 9, 0)\n }\n choix = choice([true, false])\n texte = consigne1\n if (b === 0) { texte += `$\\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}}=${e}$.` } else {\n texte += `${choix ? `$\\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}}=${e}$` : `$\\\\dfrac{${b}${ecritureAlgebriqueSauf1(a)}x}{${reduireAxPlusB(c, d)}}=${e}$`}. `\n } if (context.isDiaporama) {\n texteCorr = ''\n } else {\n texteCorr = 'Determining the forbidden values amounts to determining the values which cancel the denominator of the quotient, since division by $0$ does not exist.<br>'\n }\n texteCorr += `But $${reduireAxPlusB(c, d)}=0$ if and only if $x=${texFractionReduite(-d, c)}$. <br>So the set of forbidden values is $\\\\left\\\\{${texFractionReduite(-d, c)}\\\\right\\\\}$. <br>For all $x\\\\in \\\\mathbb{R}\\\\smallsetminus\\\\left\\\\{${texFractionReduite(-d, c)}\\\\right\\\\}$,<br>`\n if (b === 0) {\n texteCorr += `\n $\\\\begin{aligned}\n \\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}}&=${e}\\\\\\\\\n ${reduireAxPlusB(a, b)}&=${e}\\\\times(${reduireAxPlusB(c, d)})${sp(7)} \\\\text{ because the cross products are equal.}\\\\\\\\\n ${reduireAxPlusB(a, b)}&= ${reduireAxPlusB(e * c, e * d)}\\\\\\\\\n ${a - e * c}x&= ${e * d - b}\\\\\\\\\n x&=${texFractionReduite(e * d - b, a - e * c)}\n \\\\end{aligned}$<br>`\n } else {\n texteCorr += `\n $\\\\begin{aligned}\n ${choix ? `\\\\dfrac{${reduireAxPlusB(a, b)}}{${reduireAxPlusB(c, d)}}&=${e}` : `\\\\dfrac{${b}${ecritureAlgebriqueSauf1(a)}x}{${reduireAxPlusB(c, d)}}&=${e}`}\\\\\\\\\n ${choix ? `${reduireAxPlusB(a, b)}&=${e}\\\\times(${reduireAxPlusB(c, d)})` : `${b}${ecritureAlgebriqueSauf1(a)}x&=${e}\\\\times(${reduireAxPlusB(c, d)})`}${sp(7)}\\\\text{ because the cross products are equal.}\\\\\\\\\n ${reduireAxPlusB(a, b)}&= ${reduireAxPlusB(e * c, e * d)}\\\\\\\\\n ${a - e * c}x&= ${e * d - b}\\\\\\\\\n x&=${texFractionReduite(e * d - b, a - e * c)}\n \\\\end{aligned}$<br>`\n }\n\n if (-d * (a - e * c) - c * (e * d - b) === 0) {\n texteCorr += `$${texFractionReduite(e * d - b, a - e * c)}$ is a forbidden value, so the solution set of this equation is $\\\\mathscr{S}=\\\\varnothing$. `\n } else { texteCorr += `$${texFractionReduite(e * d - b, a - e * c)}$ is not a forbidden value, so the solution set of this equation is $\\\\mathscr{S}=\\\\left\\\\{${texFractionReduite(e * d - b, a - e * c)}\\\\right\\\\}$.` }\n break\n\n case 4:// e/(ax+b)=f/(cx+d)\n a = randint(-3, 9, 0)\n b = randint(-9, 9)\n c = randint(-5, 9, 0)\n d = randint(-9, 9)\n e = randint(-9, 9, 0)\n f = randint(-9, 9, 0)\n while ((c * (f * b - a * d) === -d * (e * c - f * a)) || (a * (f * b - a * d) === -b * (e * c - f * a))) { // pas de VI sol enfin normalement :-)\n a = randint(-3, 9, 0)\n b = randint(-9, 9)\n c = randint(-5, 9, 0)\n d = randint(-9, 9)\n e = randint(-9, 9, 0)\n f = randint(-9, 9, 0)\n }\n\n if (e * c - f * a === 0) { e = e + 10 }\n choix = choice([true, false])\n texte = consigne1\n texte += `$\\\\dfrac{${e}}{${reduireAxPlusB(a, b)}}=\\\\dfrac{${f}}{${reduireAxPlusB(c, d)}}$. `\n if (context.isDiaporama) {\n texteCorr = ''\n } else {\n texteCorr = 'Determining the forbidden values amounts to determining the values which cancel the denominators of the quotients, since division by $0$ does not exist.<br>'\n }\n texteCorr += `But $${reduireAxPlusB(a, b)}=0$ if and only if $x=${texFractionReduite(-b, a)}$ and $${reduireAxPlusB(c, d)}=0$ if and only if $x=${texFractionReduite(-d, c)}$. <br>So the set of forbidden values is $\\\\left\\\\{${-d / c < -b / a ? `${texFractionReduite(-d, c)}\\\\,,\\\\,${texFractionReduite(-b, a)}` : `${texFractionReduite(-b, a)}\\\\,,\\\\,${texFractionReduite(-d, c)}`}\\\\right\\\\}$. <br>`\n\n texteCorr += `For all $x\\\\in \\\\mathbb{R}\\\\smallsetminus\\\\left\\\\{${-d / c < -b / a ? `${texFractionReduite(-d, c)}\\\\,,\\\\,${texFractionReduite(-b, a)}` : `${texFractionReduite(-b, a)}\\\\,,\\\\,${texFractionReduite(-d, c)}`}\\\\right\\\\}$,<br>$\\\\begin{aligned}\\\\dfrac{${e}}{${reduireAxPlusB(a, b)}}&=\\\\dfrac{${f}}{${reduireAxPlusB(c, d)}}\\\\\\\\${f}\\\\times (${reduireAxPlusB(a, b)})&=${e}\\\\times (${reduireAxPlusB(c, d)})${sp(7)} \\\\text{ because the cross products are equal.}\\\\\\\\${reduireAxPlusB(f * a, f * b)}&=${reduireAxPlusB(e * c, e * d)}\\\\\\\\${-e * c + f * a}x&= ${e * d - f * b}\\\\\\\\x&=${texFractionReduite(-e * d + f * b, e * c - f * a)}\\\\end{aligned}$<br>`\n\n texteCorr += ` $${texFractionReduite(-e * d + f * b, e * c - f * a)}$ is not a forbidden value, so the solution set of this equation is $\\\\mathscr{S}=\\\\left\\\\{${texFractionReduite(-e * d + f * b, e * c - f * a)}\\\\right\\\\}$. `\n break\n }\n if (this.questionJamaisPosee(i, texte)) {\n // If the question has never been asked, we create another one\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n }\n this.besoinFormulaireNumerique = ['Type of equations', 3, '1: A(x)/B(x)=0\\n 2: A(x)/B(x)=a or a/A(x)=b/B(x)\\n 3: 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