{"id":503,"date":"2012-12-05T21:11:24","date_gmt":"2012-12-05T12:11:24","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=503"},"modified":"2021-09-28T20:33:23","modified_gmt":"2021-09-28T11:33:23","slug":"thr200901","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200901\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2009\uff1a\u7b2c1\u554f"},"content":{"rendered":"
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\\(a, b, c\\) \u3092\u5b9f\u6570\u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(a+b=c\\) \u3067\u3042\u308b\u3068\u304d, \\(a^3+b^3+3abc = c^3\\) \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a+b \\geqq c\\) \u3067\u3042\u308b\u3068\u304d, \\(a^3+b^3+3abc \\geqq c^3\\) \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \\[\\begin{align}\r\na^3 & +b^3-c^3+3abc \\\\\r\n& = ( a+b-c ) \\underline{( a^2+b^2+c^2 +2ab-2bc-2ca )} _ {[1]} \\\\\r\n& = 0 \\quad ( \\ \\text{\u2235} \\ a+b-c = 0 \\ )\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\na^3+b^3+3abc = c^3\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n[1] \u306b\u3064\u3044\u3066\r\n\\[\r\n[1] = \\dfrac{1}{2} \\left\\{ (a+b)^2 +(b-c)^2 +(c-a)^2 \\right\\} \\geqq 0\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\r\na^3+b^3-c^3+3abc \\geqq a+b-c \\geqq 0 \\quad ( \\ \\text{\u2235} \\ a+b-c \\geqq 0 \\ )\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\na^3+b^3+3abc \\geqq c^3\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a, b, c\\) \u3092\u5b9f\u6570\u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(a+b=c\\) \u3067\u3042\u308b\u3068\u304d, \\(a^3+b^3+3abc = c^3\\) \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b. (2)\u3000\\(a+b \\geqq c\\) \u3067\u3042\u308b … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[75],"tags":[148,15],"class_list":["post-503","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2009","tag-tohoku_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=503"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/503\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}