File: /home/mmtprep/public_html/mathzen.mmtprep.com/assets/can2F10-k2G7SUvW.js.map
{"version":3,"file":"can2F10-k2G7SUvW.js","sources":["../../src/exercices/can/2e/can2F10.js"],"sourcesContent":["import { choice } from '../../../lib/outils/arrayOutils'\nimport { miseEnEvidence } from '../../../lib/outils/embellissements'\nimport { extraireRacineCarree } from '../../../lib/outils/calculs.js'\nimport { texFractionReduite } from '../../../lib/outils/deprecatedFractions.js'\nimport { ecritureAlgebrique, ecritureParentheseSiNegatif } from '../../../lib/outils/ecritures.js'\nimport { sp } from '../../../lib/outils/outilString.js'\nimport { texNombre } from '../../../lib/outils/texNombre.js'\nimport Exercice from '../../Exercice.js'\nimport { listeQuestionsToContenu, randint, calculANePlusJamaisUtiliser } from '../../../modules/outils.js'\nimport { propositionsQcm } from '../../../lib/interactif/qcm.js'\nexport const titre = 'Résoudre une équation avec une fonction de référence*'\nexport const interactifReady = true\nexport const interactifType = 'qcm'\n\n// Les exports suivants sont optionnels mais au moins la date de publication semble essentielle\nexport const dateDePublication = '27/12/2021' // La date de publication initiale au format 'jj/mm/aaaa' pour affichage temporaire d'un tag\n\n/**\n * Modèle d'exercice très simple pour la course aux nombres\n * @author Gilles Mora\n * Référence\n*/\nexport const uuid = '1380f'\nexport const ref = 'can2F10'\nexport default function ResoudreEquationsFonctionDeReference2 () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.nbQuestions = 1\n this.tailleDiaporama = 2\n this.spacing = 2\n // Dans un exercice simple, ne pas mettre de this.listeQuestions = [] ni de this.consigne\n this.nouvelleVersion = function () {\n this.listeQuestions = []\n this.listeCorrections = []\n let texte, texteCorr, k, b, c\n for (let i = 0, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n switch (choice([1, 2, 3, 4, 5, 6])) {\n case 1 :\n b = randint(-5, 5, 0)\n c = randint(-5, 5, 0)\n k = calculANePlusJamaisUtiliser(c - b)\n if (this.interactif) {\n texte = `L'ensemble des solutions $S$ de l'équation $x^2${ecritureAlgebrique(b)}=${c}$ est :\n `\n if (k > 0) {\n if (k === 1 || k === 4 || k === 9 || k === 16 || k === 25) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{-${extraireRacineCarree(k)[0]}${sp(1)};${sp(1)}${extraireRacineCarree(k)[0]}\\\\}$`,\n statut: true\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n },\n {\n texte: `$S=\\\\{${extraireRacineCarree(k)[0]}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n if (extraireRacineCarree(k)[1] === k) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{-\\\\sqrt{${c - b}}${sp(1)};${sp(1)}\\\\sqrt{${c - b}}\\\\}$`,\n statut: true\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n },\n {\n texte: `$S=\\\\{\\\\sqrt{${c - b}}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{-${Math.sqrt(k)};${Math.sqrt(k)}\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\{${Math.sqrt(k)}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{${k}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n }\n\n if (k === 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\{0\\\\}$',\n statut: true\n },\n {\n texte: '$S=\\\\{1}\\\\}$',\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n }\n if (k < 0) {\n if (k === -1 || k === -4 || k === -9 || k === -16 || k === -25) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: `$S=\\\\{-${Math.sqrt(-k)};${Math.sqrt(-k)}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{-${Math.sqrt(-k)}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: `$S=\\\\{-\\\\sqrt{${-k}};\\\\sqrt{${-k}}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{\\\\sqrt{${-k}}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n\n texte += propositionsQcm(this, i).texte\n } else {\n texte = `Résoudre dans $\\\\mathbb{R}$ :<br>\n \n $x^2${ecritureAlgebrique(b)}=${c}$`\n }\n\n if (b > 0) {\n texteCorr = `On isole $x^2$ :<br>\n \n $\\\\begin{aligned}\n x^2${ecritureAlgebrique(b)}&=${c}\\\\\\\\\n x^2${ecritureAlgebrique(b)}-${miseEnEvidence(b)}&=${c}-${miseEnEvidence(b)}\\\\\\\\\n x^2&=${c - b}\n \\\\end{aligned}$`\n } else {\n texteCorr = `On isole $x^2$ :<br>\n \n $\\\\begin{aligned}\n x^2${ecritureAlgebrique(b)}&=${c}\\\\\\\\\n x^2${ecritureAlgebrique(b)}+${miseEnEvidence(-b)}&=${c}+${miseEnEvidence(-b)}\\\\\\\\\n x^2&=${c - b}\n \\\\end{aligned}$`\n }\n if (k > 0) {\n if (k === 1 || k === 4 || k === 9 || k === 16 || k === 25) {\n texteCorr += `<br>L'équation est de la forme $x^2=k$ avec $k=${texNombre(k)}>0$, donc l'équation a deux solutions : $-\\\\sqrt{${texNombre(k)}}$ et $\\\\sqrt{${texNombre(k)}}$.\n <br> Comme $-\\\\sqrt{${texNombre(k)}}=-${extraireRacineCarree(k)[0]}$ et $\\\\sqrt{${k}}=${extraireRacineCarree(k)[0]}$ alors\n les solutions de l'équation peuvent s'écrire plus simplement : $-${extraireRacineCarree(k)[0]}$ et $${extraireRacineCarree(k)[0]}$.<br>\n Ainsi, $S=\\\\{-${extraireRacineCarree(k)[0]}${sp(1)};${sp(1)}${extraireRacineCarree(k)[0]}\\\\}$.`\n } else {\n if (extraireRacineCarree(k)[1] !== k) {\n texteCorr += `<br>L'équation est de la forme $x^2=k$ avec $k=${texNombre(k)}>0$, donc l'équation a deux solutions : $-\\\\sqrt{${texNombre(k)}}$ et $\\\\sqrt{${texNombre(k)}}$. <br>\n Comme $-\\\\sqrt{${k}}=-${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$ et $\\\\sqrt{${k}}=${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$ alors\n les solutions de l'équation peuvent s'écrire plus simplement : $-${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$ et $${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$.<br>\n Ainsi, $S=\\\\{-${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}${sp(1)};${sp(1)}${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}\\\\}$.`\n } else {\n texteCorr += `<br>L'équation est de la forme $x^2=k$ avec $k=${c - b}>0$,\n donc l'équation a deux solutions : $-\\\\sqrt{${c - b}}$ et $\\\\sqrt{${c - b}}$.<br>\n Ainsi, $S=\\\\{-\\\\sqrt{${c - b}}${sp(1)};${sp(1)}\\\\sqrt{${c - b}}\\\\}$.`\n }\n }\n }\n if (k === 0) {\n texteCorr += `\n <br>L'équation est de la forme $x^2=k$ avec $k=${texNombre(k)}$, alors l'équation a une solution : $0$.<br>\n Ainsi, $S=\\\\{0\\\\}$. `\n }\n if (k < 0) {\n texteCorr += `\n <br>L'équation est de la forme $x^2=k$ avec $k=${texNombre(c - b)}$, alors l'équation n'a pas de solution.\n <br>Ainsi, $S=\\\\emptyset$. `\n }\n this.canEnonce = `Résoudre dans $\\\\mathbb{R}$ l'équation $x^2${ecritureAlgebrique(b)}=${c}$.`\n this.canReponseACompleter = ''\n break\n case 2 :\n b = randint(-5, 5, 0)\n c = randint(-5, 5, 0)\n k = calculANePlusJamaisUtiliser(b - c)\n if (this.interactif) {\n texte = `L'ensemble des solutions $S$ de l'équation $-x^2${ecritureAlgebrique(b)}=${c}$ est :\n `\n if (k > 0) {\n if (k === 1 || k === 4 || k === 9 || k === 16 || k === 25) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{-${extraireRacineCarree(k)[0]}${sp(1)};${sp(1)}${extraireRacineCarree(k)[0]}\\\\}$`,\n statut: true\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n },\n {\n texte: `$S=\\\\{${extraireRacineCarree(k)[0]}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n if (extraireRacineCarree(k)[1] === k) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{-\\\\sqrt{${k}}${sp(1)};${sp(1)}\\\\sqrt{${k}}\\\\}$`,\n statut: true\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n },\n {\n texte: `$S=\\\\{\\\\sqrt{${k}}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{-${Math.sqrt(k)};${Math.sqrt(k)}\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\{${Math.sqrt(k)}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{${k}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n }\n\n if (k === 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\{0\\\\}$',\n statut: true\n },\n {\n texte: '$S=\\\\{1}\\\\}$',\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n }\n if (k < 0) {\n if (k === -1 || k === -4 || k === -9 || k === -16 || k === -25) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: `$S=\\\\{-${Math.sqrt(-k)};${Math.sqrt(-k)}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{-${Math.sqrt(-k)}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: `$S=\\\\{-\\\\sqrt{${-k}};\\\\sqrt{${-k}}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{\\\\sqrt{${-k}}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n\n texte += propositionsQcm(this, i).texte\n } else {\n texte = `Résoudre dans $\\\\mathbb{R}$ :<br>\n \n $-x^2${ecritureAlgebrique(b)}=${c}$`\n }\n\n if (b > 0) {\n texteCorr = `On isole $x^2$ :<br>\n \n $\\\\begin{aligned}\n -x^2${ecritureAlgebrique(b)}&=${c}\\\\\\\\\n -x^2${ecritureAlgebrique(b)}-${miseEnEvidence(b)}&=${c}-${miseEnEvidence(b)}\\\\\\\\\n x^2&=${b - c}\n \\\\end{aligned}$`\n } else {\n texteCorr = `On isole $x^2$ :<br>\n \n $\\\\begin{aligned}\n -x^2${ecritureAlgebrique(b)}&=${c}\\\\\\\\\n - x^2${ecritureAlgebrique(b)}+${miseEnEvidence(-b)}&=${c}+${miseEnEvidence(-b)}\\\\\\\\\n x^2&=${b - c}\n \\\\end{aligned}$`\n }\n if (k > 0) {\n if (k === 1 || k === 4 || k === 9 || k === 16 || k === 25) {\n texteCorr += `<br>\n \n L'équation est de la forme $x^2=k$ avec $k=${texNombre(k)}>0$, donc l'équation a deux solutions : $-\\\\sqrt{${texNombre(k)}}$ et $\\\\sqrt{${texNombre(k)}}$.\n <br> Comme $-\\\\sqrt{${texNombre(k)}}=-${extraireRacineCarree(k)[0]}$ et $\\\\sqrt{${k}}=${extraireRacineCarree(k)[0]}$ alors\n les solutions de l'équation peuvent s'écrire plus simplement : $-${extraireRacineCarree(k)[0]}$ et $${extraireRacineCarree(k)[0]}$.<br>\n Ainsi, $S=\\\\{-${extraireRacineCarree(k)[0]}${sp(1)};${sp(1)}${extraireRacineCarree(k)[0]}\\\\}$.`\n } else {\n if (extraireRacineCarree(k)[1] !== k) {\n texteCorr += `<br>\n L'équation est de la forme $x^2=k$ avec $k=${texNombre(k)}>0$, donc l'équation a deux solutions : $-\\\\sqrt{${texNombre(k)}}$ et $\\\\sqrt{${texNombre(k)}}$. <br>\n Comme $-\\\\sqrt{${k}}=-${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$ et $\\\\sqrt{${k}}=${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$ alors\n les solutions de l'équation peuvent s'écrire plus simplement : $-${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$ et $${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}$.<br>\n Ainsi, $S=\\\\{-${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}${sp(1)};${sp(1)}${extraireRacineCarree(k)[0]}\\\\sqrt{${extraireRacineCarree(k)[1]}}\\\\}$.`\n } else {\n texteCorr += `<br>\n L'équation est de la forme $x^2=k$ avec $k=${k}>0$,\n donc l'équation a deux solutions : $-\\\\sqrt{${k}}$ et $\\\\sqrt{${k}}$.<br>\n Ainsi, $S=\\\\{-\\\\sqrt{${k}}${sp(1)};${sp(1)}\\\\sqrt{${k}}\\\\}$.`\n }\n }\n }\n if (k === 0) {\n texteCorr += `<br>\n L'équation est de la forme $x^2=k$ avec $k=${texNombre(k)}$, alors l'équation a une solution : $0$.<br>\n Ainsi, $S=\\\\{0\\\\}$. `\n }\n if (k < 0) {\n texteCorr += `<br>\n L'équation est de la forme $x^2=k$ avec $k=${texNombre(k)}$, alors l'équation n'a pas de solution.\n <br>Ainsi, $S=\\\\emptyset$. `\n }\n this.canEnonce = `Résoudre dans $\\\\mathbb{R}$ l'équation $-x^2${ecritureAlgebrique(b)}=${c}$.`\n this.canReponseACompleter = ''\n break\n\n case 3 :\n b = randint(-5, 5, 0)\n c = randint(-5, 5)\n k = calculANePlusJamaisUtiliser(c - b)\n if (this.interactif) {\n texte = `L'ensemble des solutions $S$ de l'équation $\\\\sqrt{x}${ecritureAlgebrique(b)}=${c}$ est :\n `\n if (k > 0) {\n if (k !== 1) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{${k ** 2}\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\{${2 * k}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{${k}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{${k}\\\\}$`,\n statut: true\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n },\n {\n texte: `$S=\\\\{${2 * k}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n\n if (k < 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: `$S=\\\\{\\\\sqrt{${-k}}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{${k ** 2}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n if (k === 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\{0\\\\}$',\n statut: true\n },\n {\n texte: `$S=\\\\{${k + 1}\\\\}$`,\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n }\n\n texte += propositionsQcm(this, i).texte\n } else {\n texte = `Résoudre dans $[0${sp(1)};${sp(1)}+\\\\infty[$ :<br>\n \n $\\\\sqrt{x}${ecritureAlgebrique(b)}=${c}$`\n }\n if (b > 0) {\n texteCorr = `\n \n On isole $\\\\sqrt{x}$ dans le membre de gauche pour obtenir une équation du type $\\\\sqrt{x}=k$.<br>\n $\\\\begin{aligned}\n \\\\sqrt{x}${ecritureAlgebrique(b)}&=${c}\\\\\\\\\n \\\\sqrt{x}${ecritureAlgebrique(b)}-${miseEnEvidence(b)}&=${c}-${miseEnEvidence(b)}\\\\\\\\\n \\\\sqrt{x}&=${c - b}\n \\\\end{aligned}$<br>`\n } else {\n texteCorr = `\n \n On isole $\\\\sqrt{x}$ dans le membre de gauche pour obtenir une équation du type $\\\\sqrt{x}=k$.<br>\n $\\\\begin{aligned}\n \\\\sqrt{x}${ecritureAlgebrique(b)}&=${c}\\\\\\\\\n \\\\sqrt{x}${ecritureAlgebrique(b)}+${miseEnEvidence(-b)}&=${c}+${miseEnEvidence(-b)}\\\\\\\\\n \\\\sqrt{x}&=${c - b}\n \\\\end{aligned}$<br>`\n }\n if (c - b < 0) {\n texteCorr += `\n L'équation est de la forme $\\\\sqrt{x}=k$ avec $k=${k}$. Comme $${k}<0$ alors l'équation n'admet pas de solution. <br>\n Ainsi, $S=\\\\emptyset$.<br>\n `\n }\n if (c - b > 0 || c - b === 0) {\n texteCorr += `\n L'équation est de la forme $\\\\sqrt{x}=k$ avec $k=${c - b}$. Comme $${c - b}\\\\geqslant 0$ alors l'équation admet une solution : $${k}^2=${k ** 2}$.<br>\n Ainsi $S=\\\\{${k ** 2}\\\\}$.\n `\n }\n this.canEnonce = `Résoudre dans $[0${sp(1)};${sp(1)}+\\\\infty[$ l'équation $\\\\sqrt{x}${ecritureAlgebrique(b)}=${c}$.`\n this.canReponseACompleter = ''\n break\n case 4 :\n b = randint(-5, 5, 0)\n c = randint(-5, 5)\n k = calculANePlusJamaisUtiliser(b - c)\n if (this.interactif) {\n texte = `L'ensemble des solutions $S$ de l'équation $${b}-\\\\sqrt{x}=${c}$ est :\n `\n if (k > 0) {\n if (k !== 1) {\n if (k === 2) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{${k ** 2}\\\\}$`,\n statut: true\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n },\n {\n texte: `$S=\\\\{${k}\\\\}$`,\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{${k ** 2}\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\{${2 * k}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{${k}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\{${k}\\\\}$`,\n statut: true\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n },\n {\n texte: `$S=\\\\{${2 * k}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n\n if (k < 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: `$S=\\\\{\\\\sqrt{${-k}}\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\{${k ** 2}\\\\}$`,\n statut: false\n }\n ]\n }\n }\n if (k === 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\{0\\\\}$',\n statut: true\n },\n {\n texte: `$S=\\\\{${k + 1}\\\\}$`,\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n }\n\n texte += propositionsQcm(this, i).texte\n } else {\n texte = `Résoudre dans $[0${sp(1)};${sp(1)}+\\\\infty[$ :<br>\n \n $-\\\\sqrt{x}${ecritureAlgebrique(b)}=${c}$`\n }\n if (b > 0) {\n texteCorr = `On isole $\\\\sqrt{x}$ dans le membre de gauche pour obtenir une équation du type $\\\\sqrt{x}=k$.<br>\n $\\\\begin{aligned}\n ${b}-\\\\sqrt{x}&=${c}\\\\\\\\\n ${b}-\\\\sqrt{x}-${miseEnEvidence(b)}&=${c}-${miseEnEvidence(b)}\\\\\\\\\n -\\\\sqrt{x}&=${c - b}\\\\\\\\\n \\\\sqrt{x}&=${b - c}\n \\\\end{aligned}$<br>`\n } else {\n texteCorr = `On isole $\\\\sqrt{x}$ dans le membre de gauche pour obtenir une équation du type $\\\\sqrt{x}=k$.<br>\n $\\\\begin{aligned}\n ${b}-\\\\sqrt{x}&=${c}\\\\\\\\\n ${b}-\\\\sqrt{x}+${miseEnEvidence(-b)}&=${c}+${miseEnEvidence(-b)}\\\\\\\\\n -\\\\sqrt{x}&=${c - b}\\\\\\\\\n \\\\sqrt{x}&=${b - c}\n \\\\end{aligned}$<br>`\n }\n if (k < 0) {\n texteCorr += `L'équation est de la forme $\\\\sqrt{x}=k$ avec $k=${k}$. Comme $${k}<0$ alors l'équation n'admet pas de solution. <br>\n Ainsi, $S=\\\\emptyset$.<br>\n `\n }\n if (k > 0 || k === 0) {\n texteCorr += `L'équation est de la forme $\\\\sqrt{x}=k$ avec $k=${b - c}$. Comme $${b - c}\\\\geqslant0$ alors l'équation admet une solution : $${k}^2=${k ** 2}$.<br>\n Ainsi $S=\\\\{${k ** 2}\\\\}$.\n `\n }\n this.canEnonce = `Résoudre dans $[0${sp(1)};${sp(1)}+\\\\infty[$ l'équation $-\\\\sqrt{x}${ecritureAlgebrique(b)}=${c}$.`\n this.canReponseACompleter = ''\n break\n case 5 :\n b = randint(-10, 10, 0)\n c = randint(-10, 10)\n k = c - b\n if (this.interactif) {\n texte = `L'ensemble des solutions $S$ de l'équation $\\\\dfrac{1}{x}${ecritureAlgebrique(b)}=${c}$ est :\n `\n if (k !== 0) {\n if (k === 1) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, -k)}\\\\right\\\\}$`,\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n } else {\n if (k === -1) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, -k)}\\\\right\\\\}$`,\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, -k)}\\\\right\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\left\\\\{${k}\\\\right\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n }\n\n if (k === 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: '$S=\\\\left\\\\{0\\\\right\\\\}$',\n statut: false\n },\n {\n texte: '$S=\\\\left\\\\{-1\\\\right\\\\}$',\n statut: false\n }\n ]\n }\n }\n texte += propositionsQcm(this, i).texte\n } else {\n texte = `\n Résoudre dans $\\\\mathbb{R}^*$ :<br>\n \n $\\\\dfrac{1}{x}${ecritureAlgebrique(b)}=${c}$`\n }\n\n texteCorr = `On isole $\\\\dfrac{1}{x}$ dans le membre de gauche pour obtenir une équation du type $\\\\dfrac{1}{x}=k$.<br>\n $\\\\begin{aligned}\n \\\\dfrac{1}{x}${ecritureAlgebrique(b)}&=${c}\\\\\\\\\n \\\\dfrac{1}{x}${ecritureAlgebrique(b)}+${miseEnEvidence(ecritureParentheseSiNegatif(-b))}&=${c}+${miseEnEvidence(-b)}\\\\\\\\\n \\\\dfrac{1}{x}&=${c - b}\n \\\\end{aligned}$<br>`\n\n if (k === 0) {\n texteCorr += `L'équation est de la forme $\\\\dfrac{1}{x}=k$ avec $k=${k}$. Donc l'équation n'admet pas de solution.<br>\n Ainsi, $S=\\\\emptyset$.\n `\n }\n if (k !== 0) {\n texteCorr += `$k=${k}$ et $${k}\\\\neq 0$, donc l'équation est de la forme $\\\\dfrac{1}{x}=k$ avec $k=${k}$. Donc l'équation admet une solution :\n $${texFractionReduite(1, k)}$.<br>\n Ainsi $S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$.\n `\n }\n this.canEnonce = `Résoudre dans $\\\\mathbb{R}^*$ l'équation $\\\\dfrac{1}{x}${ecritureAlgebrique(b)}=${c}$.`\n this.canReponseACompleter = ''\n break\n case 6 :\n b = randint(-10, 10, 0)\n c = randint(-10, 10)\n k = b - c\n if (this.interactif) {\n texte = `L'ensemble des solutions $S$ de l'équation $${b}-\\\\dfrac{1}{x}=${c}$ est :\n `\n if (k !== 0) {\n if (k === 1) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, -k)}\\\\right\\\\}$`,\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n } else {\n if (k === -1) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, -k)}\\\\right\\\\}$`,\n statut: false\n },\n {\n texte: '$S=\\\\emptyset$',\n statut: false\n }\n ]\n }\n } else {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$`,\n statut: true\n },\n {\n texte: `$S=\\\\left\\\\{${texFractionReduite(1, -k)}\\\\right\\\\}$`,\n statut: false\n },\n {\n texte: `$S=\\\\left\\\\{${k}\\\\right\\\\}$`,\n statut: false\n }\n ]\n }\n }\n }\n }\n\n if (k === 0) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: '$S=\\\\emptyset$',\n statut: true\n },\n {\n texte: '$S=\\\\left\\\\{0\\\\right\\\\}$',\n statut: false\n },\n {\n texte: '$S=\\\\left\\\\{-1\\\\right\\\\}$',\n statut: false\n }\n ]\n }\n }\n texte += propositionsQcm(this, i).texte\n } else {\n texte = `\n Résoudre dans $\\\\mathbb{R}^*$ :<br>\n \n $${b}-\\\\dfrac{1}{x}=${c}$`\n }\n\n texteCorr = `On isole $\\\\dfrac{1}{x}$ dans le membre de gauche pour obtenir une équation du type $\\\\dfrac{1}{x}=k$.<br>\n $\\\\begin{aligned}\n ${b}-\\\\dfrac{1}{x}&=${c}\\\\\\\\\n ${b}-\\\\dfrac{1}{x}+${miseEnEvidence(ecritureParentheseSiNegatif(-b))}&=${c}+${miseEnEvidence(ecritureParentheseSiNegatif(-b))}\\\\\\\\\n \\\\dfrac{1}{x}&=${b - c}\n \\\\end{aligned}$<br>`\n\n if (k === 0) {\n texteCorr += `L'équation est de la forme $\\\\dfrac{1}{x}=k$ avec $k=${k}$. Donc l'équation n'admet pas de solution.<br>\n Ainsi, $S=\\\\emptyset$.\n `\n }\n if (k !== 0) {\n texteCorr += `$k=${k}$ et $${k}\\\\neq 0$, donc l'équation est de la forme $\\\\dfrac{1}{x}=k$ avec $k=${k}$. Donc l'équation admet une solution :\n $${texFractionReduite(1, k)}$.<br>\n Ainsi $S=\\\\left\\\\{${texFractionReduite(1, k)}\\\\right\\\\}$.\n `\n }\n this.canEnonce = `Résoudre dans $\\\\mathbb{R}^*$ l'équation $${b}-\\\\dfrac{1}{x}=${c}$.`\n this.canReponseACompleter = ''\n break\n }\n if (this.questionJamaisPosee(i, k, b, c)) {\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n listeQuestionsToContenu(this)\n i++\n }\n cpt++\n }\n 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