{"id":1556,"date":"2016-08-16T23:56:08","date_gmt":"2016-08-16T22:56:08","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=1556"},"modified":"2018-02-17T02:05:53","modified_gmt":"2018-02-17T01:05:53","slug":"demontrer-une-egalite","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/demontrer-une-egalite\/","title":{"rendered":"D\u00e9montrer une \u00e9galit\u00e9"},"content":{"rendered":"

Objectif :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n

Utiliser diff\u00e9rentes m\u00e9thodes pour d\u00e9montrer une \u00e9galit\u00e9.<\/p>\n

 <\/p>\n

M\u00e9thode 1 :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n

On transforme par \u00e9tapes successives un membre de l\u2019\u00e9galit\u00e9 \u00e0 \u00e9tablir pour obtenir le second.<\/p>\n

    \n
  1. Prouver par cette m\u00e9thode que \"demontrer_egalite<\/li>\n
  2. Prouver que, quel que soit le nombre r\u00e9el x<\/em>,\"demontrer_egalite<\/li>\n<\/ol>\n

     <\/p>\n

    M\u00e9thode 2 :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n

    On transforme chaque membre de l\u2019\u00e9galit\u00e9 pour montrer qu\u2019ils sont \u00e9gaux \u00e0 un m\u00eame r\u00e9el.<\/p>\n

    D\u00e9montrer par cette m\u00e9thode que, pour tout r\u00e9el x<\/em>,<\/p>\n

    \"demontrer_egalite<\/p>\n

     <\/p>\n

    Applications :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n

      \n
    1. D\u00e9montrer que la diff\u00e9rence des carr\u00e9s de deux entiers cons\u00e9cutifs est \u00e9gale \u00e0 la somme de ces deux entiers.<\/li>\n
    2. D\u00e9montrer que tout nombre impair est la diff\u00e9rence des carr\u00e9s de deux nombres cons\u00e9cutifs.<\/li>\n
    3. Lorsque l\u2019on augmente de 1 le produit de quatre nombres entiers cons\u00e9cutifs, obtient-on un carr\u00e9 parfait ?<\/li>\n<\/ol>\n

       <\/p>\n

      Fiche \u00e9l\u00e8ve D\u00e9montrer une \u00e9galit\u00e9 word<\/a><\/p>\n

      Fiche \u00e9l\u00e8ve D\u00e9montrer une \u00e9galit\u00e9 pdf<\/a><\/p>\n

       <\/p>\n

       <\/p>\n","protected":false},"excerpt":{"rendered":"

      Objectif :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Utiliser diff\u00e9rentes m\u00e9thodes pour d\u00e9montrer une \u00e9galit\u00e9.   M\u00e9thode 1 :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 On transforme par \u00e9tapes successives un membre de l\u2019\u00e9galit\u00e9 \u00e0 \u00e9tablir pour obtenir le second. Prouver par cette m\u00e9thode que Prouver que, quel que soit le nombre r\u00e9el x,   M\u00e9thode 2 :\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 On transforme chaque membre de l\u2019\u00e9galit\u00e9 pour montrer qu\u2019ils … <\/p>\n

      Lire la suite<\/a><\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[23,22],"tags":[],"class_list":["post-1556","post","type-post","status-publish","format-standard","hentry","category-seconde","category-lycee","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1556","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/comments?post=1556"}],"version-history":[{"count":4,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1556\/revisions"}],"predecessor-version":[{"id":1564,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1556\/revisions\/1564"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=1556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=1556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=1556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}