{"id":1895,"date":"2023-11-22T20:36:33","date_gmt":"2023-11-22T19:36:33","guid":{"rendered":"http:\/\/localhost:8080\/maxblog\/?p=1895"},"modified":"2023-11-22T23:55:22","modified_gmt":"2023-11-22T22:55:22","slug":"utiliser-le-calcul-litteral","status":"publish","type":"post","link":"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/","title":{"rendered":"Utiliser le calcul litte\u0301ral"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1895\" class=\"elementor elementor-1895\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7d71a4a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d71a4a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-389cd7d\" data-id=\"389cd7d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a8169f1 elementor-widget elementor-widget-spacer\" data-id=\"a8169f1\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7643655 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7643655\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f297427\" data-id=\"f297427\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-361d80f elementor-widget elementor-widget-heading\" data-id=\"361d80f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-xl\">Utiliser le calcul litt\u00e9ral<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c2bda19 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c2bda19\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d178bc4\" data-id=\"d178bc4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de06178 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de06178\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cc24190\" data-id=\"cc24190\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b7c611b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7c611b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9a7e2c2\" data-id=\"9a7e2c2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fffe349 nc-justify-text elementor-widget elementor-widget-text-editor\" data-id=\"fffe349\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#Introduction\" >Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#Cours\" >Cours<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#1_Regles_de_calcul_sur_les_puissances_entieres_relatives_et_sur_les_racines_carrees\" >1. R\u00e8gles de calcul sur les puissances enti\u00e8res relatives et sur les\nracines carr\u00e9es<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#2_Identites_remarquables\" >2. Identit\u00e9s remarquables<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#3_Exemples_de_calcul_sur_des_expressions_algebriques\" >3. Exemples de calcul sur des expressions alg\u00e9briques<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#4_Somme_dinegalites_et_produit_dune_inegalite_par_un_reel\" >4. Somme d\u2019in\u00e9galit\u00e9s et produit d\u2019une in\u00e9galit\u00e9 par un r\u00e9el<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#5_Ensemble_des_solutions_dune_equation_dune_inequation\" >5. Ensemble des solutions d\u2019une \u00e9quation, d\u2019une in\u00e9quation<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#Methodes\" >M\u00e9thodes<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#1_Effectuer_des_calculs_numeriques_ou_litteraux_avec_des_puissances_des_racines_carrees_et_des_ecritures_fractionnaires\" >1. Effectuer des calculs num\u00e9riques ou litt\u00e9raux avec des puissances, des\nracines carr\u00e9es et des \u00e9critures fractionnaires :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#2_Exprimer_une_variable_en_fonction_des_autres\" >2. Exprimer une variable en fonction des autres :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#3_Choisir_la_forme_la_plus_adaptee_dune_expression\" >3. Choisir la forme la plus adapt\u00e9e d\u2019une expression :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#4_Comparer_deux_quantites_en_utilisant_leur_difference_ou_leur_quotient\" >4. Comparer deux quantit\u00e9s en utilisant leur diff\u00e9rence ou leur quotient :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#5_Modeliser_un_probleme_par_une_inequation\" >5. Mod\u00e9liser un probl\u00e8me par une in\u00e9quation :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-le-calcul-litteral\/#6_Resoudre_une_inequation_du_premier_degre\" >6. R\u00e9soudre une in\u00e9quation du premier degr\u00e9 :<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Le calcul litt\u00e9ral consiste \u00e0 manipuler des expressions\nmath\u00e9matiques contenant des lettres (souvent not\u00e9es <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span>,\n<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>, etc.) qui repr\u00e9sentent des nombres\ninconnus. Cette branche des math\u00e9matiques est tr\u00e8s utile pour r\u00e9soudre des\nprobl\u00e8mes de mani\u00e8re g\u00e9n\u00e9rale sans conna\u00eetre les valeurs sp\u00e9cifiques.<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Cours\"><\/span>Cours<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Regles_de_calcul_sur_les_puissances_entieres_relatives_et_sur_les_racines_carrees\"><\/span>1. R\u00e8gles de calcul sur les puissances enti\u00e8res relatives et sur les\nracines carr\u00e9es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Puissances :<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/b><\/p>\n\n<p class=\"MsoNormal\"><span lang=\"EN-US\" style=\"mso-ansi-language:EN-US\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">a^m \\times a^n = a^{m+n}<\/span><\/span><\/p>\n\n<p class=\"MsoNormal\"><span lang=\"EN-US\" style=\"mso-ansi-language:EN-US\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">a^m \\div a^n = a^{m-n}<\/span>,\n<span class=\"katex-eq\" data-katex-display=\"false\">a \\neq 0<\/span><\/span><\/p>\n\n<p class=\"MsoNormal\"><span lang=\"EN-US\" style=\"mso-ansi-language:EN-US\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">(a^m)^n = a^{m \\times n}<\/span><\/span><\/p>\n\n<p class=\"MsoNormal\"><span lang=\"EN-US\" style=\"mso-ansi-language:EN-US\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">a^0 = 1<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">a\n\\neq 0<\/span><\/span><\/p>\n\n<p class=\"MsoNormal\"><span lang=\"EN-US\" style=\"mso-ansi-language:EN-US\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span><\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">a^{-n} = \\frac{1}{a^n}<\/span>,\n<span class=\"katex-eq\" data-katex-display=\"false\">a \\neq 0<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Racines carr\u00e9es :<\/b><\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{a \\times b} = \\sqrt{a}\n\\times \\sqrt{b}<\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{\\frac{a}{b}} =\n\\frac{\\sqrt{a}}{\\sqrt{b}}<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">b \\neq 0<\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{a^2} = |a|<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Identites_remarquables\"><\/span>2. Identit\u00e9s remarquables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Diff\u00e9rence de carr\u00e9s :<\/b> <span class=\"katex-eq\" data-katex-display=\"false\">a^2 &#8211; b^2 = (a &#8211; b)(a\n+ b)<\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Carr\u00e9 d&rsquo;une somme :<\/b> <span class=\"katex-eq\" data-katex-display=\"false\">(a + b)^2 = a^2 + 2ab + b^2<\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Carr\u00e9 d&rsquo;une diff\u00e9rence :<\/b> <span class=\"katex-eq\" data-katex-display=\"false\">(a &#8211; b)^2 = a^2 &#8211; 2ab + b^2<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Utilisation dans les deux sens :<\/b><\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Pour factoriser : <span class=\"katex-eq\" data-katex-display=\"false\">x^2 &#8211; 9 =\n(x &#8211; 3)(x + 3)<\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Pour d\u00e9velopper : <span class=\"katex-eq\" data-katex-display=\"false\">(x &#8211; 2)^2 =\nx^2 &#8211; 4x + 4<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"3_Exemples_de_calcul_sur_des_expressions_algebriques\"><\/span>3. Exemples de calcul sur des expressions alg\u00e9briques<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Simplification : <\/b><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{2x^2 &#8211; 4x}{2x} =\n\\frac{2x(x &#8211; 2)}{2x} = x &#8211; 2<\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>D\u00e9veloppement et factorisation :<\/b> <span class=\"katex-eq\" data-katex-display=\"false\">(x + 3)(x &#8211; 2) = x^2 + x &#8211; 6<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"4_Somme_dinegalites_et_produit_dune_inegalite_par_un_reel\"><\/span>4. Somme d\u2019in\u00e9galit\u00e9s et produit d\u2019une in\u00e9galit\u00e9 par un r\u00e9el<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Somme :<\/b> Si <span class=\"katex-eq\" data-katex-display=\"false\">a &gt; b<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">c &gt;\nd<\/span>, alors <span class=\"katex-eq\" data-katex-display=\"false\">a + c &gt; b + d<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Produit par un r\u00e9el positif :<\/b> Si <span class=\"katex-eq\" data-katex-display=\"false\">a &gt; b<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">c\n&gt; 0<\/span>, alors <span class=\"katex-eq\" data-katex-display=\"false\">a \\times c &gt; b \\times c<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Produit par un r\u00e9el n\u00e9gatif<\/b> <b>:<\/b> Si <span class=\"katex-eq\" data-katex-display=\"false\">a &gt; b<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">c\n&lt; 0<\/span>, alors <span class=\"katex-eq\" data-katex-display=\"false\">a \\times c &lt; b \\times c<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"5_Ensemble_des_solutions_dune_equation_dune_inequation\"><\/span>5. Ensemble des solutions d\u2019une \u00e9quation, d\u2019une in\u00e9quation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>\u00c9quation :<\/b><\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Une \u00e9quation est une expression o\u00f9\ndeux quantit\u00e9s sont \u00e9gales, souvent contenant une ou plusieurs inconnues.\nR\u00e9soudre une \u00e9quation revient \u00e0 trouver l&rsquo;ensemble des valeurs que peut prendre\nl&rsquo;inconnue pour que l&rsquo;\u00e9galit\u00e9 soit vraie.<\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Par exemple, pour l&rsquo;\u00e9quation <span class=\"katex-eq\" data-katex-display=\"false\">2x\n&#8211; 4 = 0<\/span>, la solution est <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span>, car cette valeur rend\nl&rsquo;\u00e9galit\u00e9 vraie. L&rsquo;ensemble des solutions est donc <span class=\"katex-eq\" data-katex-display=\"false\">S = \\{2\\}<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Une \u00e9quation peut aussi avoir\nplusieurs solutions, une infinit\u00e9 de solutions, ou aucune solution.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>In\u00e9quation :<\/b><\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Une in\u00e9quation est similaire \u00e0 une\n\u00e9quation mais, au lieu d&rsquo;une \u00e9galit\u00e9, elle exprime une relation d&rsquo;ordre (&gt;,\n&lt;, \u2265, \u2264) entre deux expressions.<\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; L&rsquo;objectif est de d\u00e9terminer\nl&rsquo;ensemble des valeurs que peut prendre l&rsquo;inconnue pour que l&rsquo;in\u00e9quation soit\nvraie.<\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Par exemple, pour l&rsquo;in\u00e9quation <span class=\"katex-eq\" data-katex-display=\"false\">2x\n&#8211; 4 &gt; 0<\/span>, la solution est <span class=\"katex-eq\" data-katex-display=\"false\">x &gt; 2<\/span>, car toutes les\nvaleurs de <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> sup\u00e9rieures \u00e0 2 rendent l&rsquo;in\u00e9quation vraie.\nL&rsquo;ensemble des solutions est donc <span class=\"katex-eq\" data-katex-display=\"false\">S = ]2, +\\infty[<\/span>. <\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Methodes\"><\/span>M\u00e9thodes<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Effectuer_des_calculs_numeriques_ou_litteraux_avec_des_puissances_des_racines_carrees_et_des_ecritures_fractionnaires\"><\/span>1. Effectuer des calculs num\u00e9riques ou litt\u00e9raux avec des puissances, des\nracines carr\u00e9es et des \u00e9critures fractionnaires :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Puissances :<\/b> Utilisez les r\u00e8gles des puissances\npour simplifier l&rsquo;expression.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span><span lang=\"EN-US\" style=\"mso-ansi-language:EN-US\">&#8211; Exemple : <span class=\"katex-eq\" data-katex-display=\"false\">a^2 \\times a^3 = a^{2+3} =\na^5<\/span>.<\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Racines carr\u00e9es :<\/b> Appliquez les propri\u00e9t\u00e9s des racines carr\u00e9es pour\nsimplifier.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{9}\n= 3<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{a^2} = |a|<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>\u00c9critures fractionnaires :<\/b> Simplifiez les fractions en trouvant le\nPGCD des num\u00e9rateurs et d\u00e9nominateurs, ou effectuez des simplifications\ncrois\u00e9es.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{2x^2}{4x}\n= \\frac{x}{2}<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Exprimer_une_variable_en_fonction_des_autres\"><\/span>2. Exprimer une variable en fonction des autres :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Cas simples :<\/b> Isoler la variable d\u00e9sir\u00e9e en\nutilisant des op\u00e9rations de base.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : <span class=\"katex-eq\" data-katex-display=\"false\">U\n= RI<\/span> donne <span class=\"katex-eq\" data-katex-display=\"false\">I = \\frac{U}{R}<\/span>, et <span class=\"katex-eq\" data-katex-display=\"false\">S = \\pi r^2<\/span>\ndonne <span class=\"katex-eq\" data-katex-display=\"false\">r = \\sqrt{\\frac{S}{\\pi}}<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Relation du premier degr\u00e9 :<\/b> R\u00e9arrangez l&rsquo;\u00e9quation pour isoler la\nvariable d\u00e9sir\u00e9e.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : <span class=\"katex-eq\" data-katex-display=\"false\">ax\n+ by = c<\/span> donne <span class=\"katex-eq\" data-katex-display=\"false\">x = \\frac{c &#8211; by}{a}<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"3_Choisir_la_forme_la_plus_adaptee_dune_expression\"><\/span>3. Choisir la forme la plus adapt\u00e9e d\u2019une expression :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Factoris\u00e9e :<\/b> Utile quand on souhaite trouver les\nracines d&rsquo;une \u00e9quation.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : <span class=\"katex-eq\" data-katex-display=\"false\">x^2\n&#8211; 6x + 9 = (x &#8211; 3)^2<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>D\u00e9velopp\u00e9e r\u00e9duite :<\/b> Utile pour simplifier ou comparer des\nexpressions.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : <span class=\"katex-eq\" data-katex-display=\"false\">(x\n&#8211; 3)^2 = x^2 &#8211; 6x + 9<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"4_Comparer_deux_quantites_en_utilisant_leur_difference_ou_leur_quotient\"><\/span>4. Comparer deux quantit\u00e9s en utilisant leur diff\u00e9rence ou leur quotient :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Diff\u00e9rence :<\/b> Si <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>\nsont deux quantit\u00e9s, alors <span class=\"katex-eq\" data-katex-display=\"false\">a &#8211; b &gt; 0<\/span> signifie que <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\nest plus grand que <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Quotient :<\/b> Si <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> sont positives,\nalors <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{a}{b} &gt; 1<\/span> signifie que <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> est plus\ngrand que <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"5_Modeliser_un_probleme_par_une_inequation\"><\/span>5. Mod\u00e9liser un probl\u00e8me par une in\u00e9quation :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; Analysez le probl\u00e8me, identifiez les variables et\n\u00e9tablissez une in\u00e9quation qui d\u00e9crit la situation.<\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : Si vous avez moins de 100\u20ac\n\u00e0 d\u00e9penser et chaque livre co\u00fbte 20\u20ac, <span class=\"katex-eq\" data-katex-display=\"false\">20x \\leq 100<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"6_Resoudre_une_inequation_du_premier_degre\"><\/span>6. R\u00e9soudre une in\u00e9quation du premier degr\u00e9 :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; Isoler la variable en effectuant des op\u00e9rations inverses\ndes deux c\u00f4t\u00e9s de l&rsquo;in\u00e9quation.<\/p>\n\n<p class=\"MsoNormal\"><br>\n<span style=\"mso-spacerun:yes\">&nbsp;&nbsp; <\/span>&#8211; Exemple : Pour r\u00e9soudre <span class=\"katex-eq\" data-katex-display=\"false\">2x +\n3 &lt; 7<\/span>, commencez par soustraire 3 des deux c\u00f4t\u00e9s, donnant <span class=\"katex-eq\" data-katex-display=\"false\">2x\n&lt; 4<\/span>, puis divisez par 2 pour obtenir <span class=\"katex-eq\" data-katex-display=\"false\">x &lt; 2<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; Il est important de noter que lorsqu&rsquo;on multiplie ou divise les deux c\u00f4t\u00e9s\nd&rsquo;une in\u00e9quation par un nombre n\u00e9gatif, le sens de l&rsquo;in\u00e9quation change (par\nexemple, de \u00ab\u00a0&gt;\u00a0\u00bb \u00e0 \u00ab\u00a0&lt;\u00ab\u00a0).<\/p>\n\n\n\n\n\n<style>@font-face\n\t{font-family:\"Cambria Math\";\n\tpanose-1:2 4 5 3 5 4 6 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:roman;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face\n\t{font-family:Calibri;\n\tpanose-1:2 15 5 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536859905 -1073732485 9 0 511 0;}@font-face\n\t{font-family:\"Calibri Light\";\n\tpanose-1:2 15 3 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-469750017 -1073732485 9 0 511 0;}p.MsoNormal, li.MsoNormal, 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class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8c43dc4\" data-id=\"8c43dc4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa0c527 elementor-widget elementor-widget-spacer\" data-id=\"aa0c527\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-789777a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"789777a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dd93843\" data-id=\"dd93843\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b1d0d5c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b1d0d5c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7e963bc\" data-id=\"7e963bc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-40909d1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"40909d1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3a01f62\" data-id=\"3a01f62\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Utiliser le calcul litt\u00e9ral Introduction &nbsp; Le calcul litt\u00e9ral consiste \u00e0 manipuler des expressions math\u00e9matiques contenant des lettres (souvent not\u00e9es , , , , etc.) qui repr\u00e9sentent des nombres inconnus. Cette branche des math\u00e9matiques est tr\u00e8s utile pour r\u00e9soudre des probl\u00e8mes de mani\u00e8re g\u00e9n\u00e9rale sans conna\u00eetre les valeurs sp\u00e9cifiques. Cours &nbsp; 1. R\u00e8gles de calcul [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_canvas","format":"standard","meta":{"footnotes":""},"categories":[25,26,5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1895"}],"collection":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/comments?post=1895"}],"version-history":[{"count":7,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1895\/revisions"}],"predecessor-version":[{"id":2024,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1895\/revisions\/2024"}],"wp:attachment":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/media?parent=1895"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/categories?post=1895"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/tags?post=1895"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}