{"id":667,"date":"2013-03-07T00:39:12","date_gmt":"2013-03-06T15:39:12","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=667"},"modified":"2021-09-29T21:26:59","modified_gmt":"2021-09-29T12:26:59","slug":"thr200701","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200701\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2007\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3057, \u6574\u5f0f \\(x^n\\) \u3092 \\(x^2-6x-12\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092 \\(a _ n x +b _ n\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(a _ 2 , b _ 2\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a _ {n+1} , b _ {n+1}\\) \u3092 \\(a _ n , b _ n\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u5404 \\(n\\) \u306b\u5bfe\u3057\u3066, \\(a _ n\\) \u3068 \\(b _ n\\) \u306e\u516c\u7d04\u6570\u3067\u7d20\u6570\u3068\u306a\u308b\u3082\u306e\u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\[\r\nx^2 = ( x^2-6x-12 ) +6x+12\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\na _ 2 =\\underline{6} , \\ b _ 2 =\\underline{12}\r\n\\]\r\n

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

    \\(x^n\\) \u3092 \\(x^2-6x-12\\) \u3067\u5272\u3063\u305f\u5546\u3092 \\(Q(x)\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nx _ n = (x^2-6x-12) Q(x) +a _ n x +b _ n\r\n\\]\r\n\u3053\u308c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nx^{n+1} & = (x^2-6x-12) x Q(x) +a _ n x^2 +b _ n x \\\\\r\n& = (x^2-6x-12) \\left\\{ x Q(x) +a _ n \\right\\} +\\left( 6 a _ n +b _ n\\right) x +12 a _ n\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\na _ {n+1} =\\underline{6 a _ n +b _ n} , \\ b _ {n+1} =\\underline{12 a _ n}\r\n\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u304b\u3089, \u3059\u3079\u3066\u306e \\(n\\) \u306b\u5bfe\u3057\u3066 \\(a _ n\\) \u3068 \\(b _ n\\) \u306e\u516c\u7d04\u6570\u3068\u306a\u308a\u3046\u308b\u7d20\u6570\u306f, \\(2\\) \u307e\u305f\u306f \\(3\\) \u3067\u3042\u308b.
    \r\n(2)<\/strong> \u306e\u7d50\u679c\u304b\u3089, \\(a _ n , b _ n\\) \u304c\u3068\u3082\u306b \\(6\\) \u306e\u500d\u6570\u3067\u3042\u308c\u3070, \\(a _ {n+1} , b _ {n+1}\\) \u3082\u3068\u3082\u306b \\(6\\) \u306e\u500d\u6570\u3068\u306a\u308b.
    \r\n\\(a _ 2 , b _ 2\\) \u304c \\(6\\) \u306e\u500d\u6570\u306a\u306e\u3067, \u5e30\u7d0d\u7684\u306b\u3059\u3079\u3066\u306e\u81ea\u7136\u6570 \\(n\\) \u306b\u3064\u3044\u3066 \\(a _ n , b _ n\\) \u306f\u3068\u3082\u306b \\(6\\) \u306e\u500d\u6570\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u7d20\u6570\u306f\r\n\\[\r\n\\underline{2 , 3}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3057, \u6574\u5f0f \\(x^n\\) \u3092 \\(x^2-6x-12\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092 \\(a _ n x +b _ n\\) \u3068\u3059\u308b. (1)\u3000\\(a _ 2 , b _ 2\\) \u3092\u6c42\u3081\u3088. … \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":[95],"tags":[148,109],"class_list":["post-667","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2007","tag-tohoku_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/667","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=667"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/667\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=667"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=667"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=667"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}