{"id":454,"date":"2012-10-29T23:23:20","date_gmt":"2012-10-29T14:23:20","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=454"},"modified":"2021-09-16T06:03:14","modified_gmt":"2021-09-15T21:03:14","slug":"ngr201004","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201004\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2010\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(xy\\) \u5e73\u9762\u4e0a\u3067 \\(x\\) \u5ea7\u6a19\u3068 \\(y\\) \u5ea7\u6a19\u304c\u3068\u3082\u306b\u6574\u6570\u3067\u3042\u308b\u70b9\u3092\u683c\u5b50\u70b9\u3068\u547c\u3076.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(y = \\dfrac{1}{3} x^2 +\\dfrac{1}{2} x\\) \u306e\u30b0\u30e9\u30d5\u4e0a\u306b\u7121\u9650\u500b\u306e\u683c\u5b50\u70b9\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a , b\\) \u306f\u5b9f\u6570\u3067 \\(a \\neq 0\\) \u3068\u3059\u308b. \\(y = ax^2+bx\\) \u306e\u30b0\u30e9\u30d5\u4e0a\u306b, \u70b9 \\((0,0)\\) \u4ee5\u5916\u306b\u683c\u5b50\u70b9\u304c \\(2\\) \u3064\u5b58\u5728\u3059\u308c\u3070, \u7121\u9650\u500b\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n

    \u89e3\u7b54<\/h3>\r\n

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

    \\(x = 6n\\) \uff08 \\(n\\) \u306f\u6574\u6570\uff09\u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\ny & = \\dfrac{1}{3} \\cdot (6n)^2 +\\dfrac{1}{2} \\cdot 6n \\\\\r\n& = 12n^2+3n\n\\end{align}\\]\r\n\u3053\u308c\u306f\u6574\u6570\u306a\u306e\u3067, \u70b9 \\(( 6n , 12n^2+3n )\\) \u306f, \\(y=\\dfrac{1}{3}x^2 +\\dfrac{1}{2}x\\) \u4e0a\u306e\u683c\u5b50\u70b9\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \\(n\\) \u306f\u7121\u9650\u306b\u3042\u308b\u306e\u3067, \u683c\u5b50\u70b9\u3082\u7121\u9650\u500b\u306b\u3042\u308b\u3068\u3044\u3048\u308b.<\/p>\r\n

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

    \\(y = ax^2+bx\\) \u4e0a\u306e \\(2\\) \u3064\u306e\u683c\u5b50\u70b9\u3092 \\((x _ 1 , y _ 1) , \\ (x _ 2 , y _ 2)\\) \uff08 \\(x _ 1 , x _ 2\\) \u306f\u4e92\u3044\u306b\u7570\u306a\u308a \\(0\\) \u3067\u306a\u3044\uff09\u3068\u304a\u304f.
    \r\n\u3053\u306e\u3068\u304d, \u6761\u4ef6\u3088\u308a\r\n\\[\r\n\\left( \\begin{array}{cc} {x _ 1}^2 & x _ 1 \\\\ {x _ 2}^2 & x _ 2 \\end{array} \\right) \\left( \\begin{array}{c} a \\\\ b \\end{array} \\right) = \\left( \\begin{array}{c} y _ 1 \\\\ y _ 2 \\end{array} \\right)\n\\]\r\n\u3053\u3053\u3067\r\n\\[\r\n\\det \\left( \\begin{array}{cc} {x _ 1}^2 & x _ 1 \\\\ {x _ 2}^2 & x _ 2 \\end{array} \\right) = x _ 1 x _ 2 ( x _ 1 -x _ 2 ) \\neq 0\n\\]\r\n\u306a\u306e\u3067\u9006\u884c\u5217 \\(\\left( \\begin{array}{cc} {x _ 1}^2 & x _ 1 \\\\ {x _ 2}^2 & x _ 2 \\end{array} \\right)^{-1}\\) \u304c\u5b58\u5728\u3057\r\n\\[\r\n\\left( \\begin{array}{c} a \\\\ b \\end{array} \\right) = \\dfrac{1}{x _ 1 x _ 2 ( x _ 1 -x _ 2 )} \\left( \\begin{array}{cc} x _ 2 & -x _ 1 \\\\ -{x _ 2}^2 & {x _ 1}^2 \\end{array} \\right) \\left( \\begin{array}{c} y _ 1 \\\\ y _ 2 \\end{array} \\right)\n\\]\r\n\\(x _ 1 , x _ 2 , y _ 1 , y _ 2\\) \u306f\u3059\u3079\u3066\u6574\u6570\u306a\u306e\u3067, \\(a , b\\) \u306f\u3068\u3082\u306b\u6709\u7406\u6570\u3067\u3042\u308b.
    \r\n\u305d\u3053\u3067, \\(a =\\dfrac{p _ 1}{q _ 1}\\) , \\(b =\\dfrac{p _ 2}{q _ 2}\\) \uff08 \\(p _ 1 , p _ 2 , q _ 1 , q _ 2\\) \u306f\u6574\u6570\uff09\u3068\u304a\u304f.
    \r\n\\(x = q _ 1 q _ 2 n\\) \uff08 \\(n\\) \u306f\u6574\u6570\uff09\u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\ny & = \\dfrac{p _ 1}{q _ 1} \\cdot (q _ 1 q _ 2 n)^2 +\\dfrac{p _ 2}{q _ 2} \\cdot q _ 1 q _ 2 n \\\\\r\n& = p _ 1 q _ 1 {q _ 2}^2 n^2 +p _ 2 q _ 1 n\n\\end{align}\\]\r\n\u3053\u308c\u306f\u6574\u6570\u306a\u306e\u3067, \u70b9 \\(( q _ 1 q _ 2 n , p _ 1 q _ 1 {q _ 2}^2 n^2 +p _ 2 q _ 1 n )\\) \u306f, \\(y = ax^2 +bx\\) \u4e0a\u306e\u683c\u5b50\u70b9\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \\(n\\) \u306f\u7121\u9650\u306b\u3042\u308b\u306e\u3067, \u683c\u5b50\u70b9\u3082\u7121\u9650\u500b\u306b\u3042\u308b\u3068\u3044\u3048\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u3067 \\(x\\) \u5ea7\u6a19\u3068 \\(y\\) \u5ea7\u6a19\u304c\u3068\u3082\u306b\u6574\u6570\u3067\u3042\u308b\u70b9\u3092\u683c\u5b50\u70b9\u3068\u547c\u3076. (1)\u3000\\(y = \\dfrac{1}{3} x^2 +\\dfrac{1}{2} x\\) \u306e\u30b0\u30e9\u30d5\u4e0a\u306b\u7121\u9650\u500b\u306e\u683c\u5b50\u70b9\u304c\u5b58\u5728 … \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":[34],"tags":[143,14],"class_list":["post-454","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2010","tag-nagoya_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/454","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=454"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/454\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=454"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=454"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}