{"id":1391,"date":"2017-02-25T01:26:34","date_gmt":"2017-02-24T16:26:34","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1391"},"modified":"2021-03-18T16:26:15","modified_gmt":"2021-03-18T07:26:15","slug":"kyr201606","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201606\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2016\uff1a\u7b2c6\u554f"},"content":{"rendered":"<hr \/>\n<p>\u8907\u7d20\u6570\u3092\u4fc2\u6570\u3068\u3059\u308b \\(2\\) \u6b21\u5f0f \\(f(x) = x^2 +ax +b\\) \u306b\u5bfe\u3057, \u6b21\u306e\u6761\u4ef6\u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p>(\u30a4)\u3000\\(f( x^3 )\\) \u306f \\(f(x)\\) \u3067\u5272\u308a\u5207\u308c\u308b.<\/p><\/li>\r\n<li><p>(\u30ed)\u3000\\(f(x)\\) \u306e\u4fc2\u6570 \\(a , b\\) \u306e\u5c11\u306a\u304f\u3068\u3082\u4e00\u65b9\u306f\u865a\u6570\u3067\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u3053\u306e \\(2\\) \u3064\u306e\u6761\u4ef6 (\u30a4), (\u30ed) \u3092\u540c\u6642\u306b\u6e80\u305f\u3059 \\(2\\) \u6b21\u5f0f\u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p>\r\n<hr\/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\\(2\\) \u6b21\u65b9\u7a0b\u5f0f \\(f(x) = 0\\) \u306e\u89e3\u3092 \\(\\alpha , \\beta\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nf( \\alpha ) = 0 , \\ f( \\beta ) = 0 \\quad ... [1]\r\n\\]\r\n\u307e\u305f, \u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\na = -\\alpha -\\beta , \\ b = \\alpha \\beta \\quad ... [2]\r\n\\]\r\n\u6761\u4ef6 (\u30a4) \u3088\u308a, \\(f( x^3 )\\) \u3092 \\(f(x)\\) \u3067\u5272\u3063\u305f\u5546\u3092 \\(P(x)\\) \u3068\u304a\u3051\u3070\r\n\\[\r\nf( x^3 ) = f(x) P(x)\r\n\\]\r\n\u3053\u308c\u306b, \\(x = \\alpha , \\beta\\) \u3092\u4ee3\u5165\u3059\u308c\u3070, [1] \u3088\u308a\r\n\\[\r\n\\left\\{ \\begin{array}{l} f( \\alpha^3 ) = f( \\alpha ) P( \\alpha ) = 0 \\\\ f( \\beta^3 ) = f( \\beta ) P( \\beta ) = 0 \\end{array} \\right.\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(\\alpha^3 , \\beta^3\\) \u3082 \\(f(x) = 0\\) \u306e\u89e3\u3067\u3042\u308b.<br \/>\r\n\\(f(x) = 0\\) \u306f\u9ad8\u3005 \\(2\\) \u3064\u306e\u89e3\u3057\u304b\u3082\u305f\u306a\u3044\u304b\u3089, \\(\\alpha^3 , \\beta^3\\) \u306f \\(\\alpha , \\beta\\) \u306e\u3044\u305a\u308c\u304b\u3067\u3042\u308a, \u4ee5\u4e0b\u306e \\(3\\) \u3064\u306e\u5834\u5408\u304c\u8003\u3048\u3089\u308c\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(( \\alpha^3 , \\beta^3 ) = ( \\alpha , \\alpha )\\)<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(( \\alpha^3 , \\beta^3 ) = ( \\alpha , \\beta )\\)<\/p><\/li>\r\n<li><p><strong>3*<\/strong>\u3000\\(( \\alpha^3 , \\beta^3 ) = ( \\beta , \\alpha )\\)<\/p><\/li>\r\n<\/ol>\r\n<p>\u305d\u308c\u305e\u308c\u306e\u5834\u5408\u306b\u3064\u3044\u3066, \u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(( \\alpha^3 , \\beta^3 ) = ( \\alpha , \\alpha )\\) \u306e\u3068\u304d<br \/>\r\n\\(\\alpha^3 = \\alpha\\) \u3088\u308a\r\n\\[\\begin{align}\r\n\\alpha ( \\alpha +1 ) ( \\alpha -1 ) & = 0 \\\\\r\n\\text{\u2234} \\quad \\alpha & = 0 , \\pm 1\r\n\\end{align}\\]\r\n<ul>\r\n<li><p>\\(\\alpha = 0\\) \u306e\u3068\u304d<br \/>\r\n\\(\\beta^3 = 0\\) \u3088\u308a \\(\\beta = 0\\) \u3068\u306a\u308a, [2] \u3088\u308a, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3055\u305a, \u4e0d\u9069.<\/p><\/li>\r\n<li><p>\\(\\alpha = 1\\) \u306e\u3068\u304d<br \/>\r\n\\(\\beta^3 = 1\\) \u3088\u308a\r\n\\[\r\n\\beta = 1 , \\dfrac{-1 \\pm \\sqrt{3} i}{2}\r\n\\]\r\n[2] \u3092\u7528\u3044\u3066, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3059\u306e\u306f\r\n\\[\r\n( a , b ) = \\left( -\\dfrac{1 \\pm \\sqrt{3} i}{2} , \\dfrac{-1 \\pm \\sqrt{3} i}{2} \\right) \\quad ( \\ \\text{\u8907\u53f7\u540c\u9806} \\ )\r\n\\]<\/li>\r\n<li><p>\\(\\alpha = -1\\) \u306e\u3068\u304d<br \/>\r\n\\(\\beta^3 = -1\\) \u3088\u308a\r\n\\[\r\n\\beta = -1 , \\dfrac{1 \\pm \\sqrt{3} i}{2}\r\n\\]\r\n[2] \u3092\u7528\u3044\u3066, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3059\u306e\u306f\r\n\\[\r\n( a , b ) = \\left( -\\dfrac{-1 \\pm \\sqrt{3} i}{2} , -\\dfrac{1 \\pm \\sqrt{3} i}{2} \\right) \\quad ( \\ \\text{\u8907\u53f7\u540c\u9806} \\ )\r\n\\]<\/li>\r\n<\/ul><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(( \\alpha^3 , \\beta^3 ) = ( \\alpha , \\beta )\\) \u306e\u3068\u304d<br \/>\r\n\\(\\alpha^3 = \\alpha\\) \u3088\u308a\r\n\\[\r\n\\alpha = 0 , \\pm 1\r\n\\]\r\n\\(\\beta^3 = \\beta\\) \u3088\u308a\r\n\\[\r\n\\beta = 0 , \\pm 1\r\n\\]\r\n\u3044\u305a\u308c\u306e\u7d44\u5408\u305b\u3082, [2] \u3088\u308a, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3055\u305a, \u4e0d\u9069.<\/p><\/li>\r\n<li><p><strong>3*<\/strong>\u3000\\(( \\alpha^3 , \\beta^3 ) = ( \\beta , \\alpha )\\) \u306e\u3068\u304d<br \/>\r\n\\(\\alpha = \\beta^3 = \\alpha^9\\) \u3088\u308a\r\n\\[\r\n\\alpha = 0 , \\pm 1 , \\pm i , \\dfrac{\\pm 1 \\pm i}{\\sqrt{2}}\r\n\\]\r\n<ul>\r\n<li><p>\\(\\alpha = 0 , \\pm 1\\) \u306e\u3068\u304d<br \/>\r\n\\(\\beta = 0 , \\pm 1\\) \u3068\u306a\u308a, [2] \u3088\u308a, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3055\u305a, \u4e0d\u9069.<\/p><\/li>\r\n<li><p>\\(\\alpha = \\pm i\\) \u306e\u3068\u304d<br \/>\r\n\\[\r\n\\beta = \\alpha^3 = \\mp i\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, [2] \u3088\u308a\r\n\\[\r\na = 0 , \\ b = 1\r\n\\]\r\n\u3053\u308c\u306f, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3055\u305a, \u4e0d\u9069.<\/p><\/li>\r\n<li><p>\\(\\alpha = \\dfrac{1 \\pm i}{\\sqrt{2}}\\) \u306e\u3068\u304d<br \/>\r\n\\[\r\n\\beta = \\alpha^3 = \\dfrac{-1 \\pm i}{\\sqrt{2}}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, [2] \u3088\u308a\r\n\\[\r\na = \\pm \\sqrt{2} i , \\ \\beta = -1\r\n\\]\r\n\u3053\u308c\u306f, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3059.<\/p><\/li>\r\n<li><p>\\(\\alpha = \\dfrac{-1 \\pm i}{\\sqrt{2}}\\) \u306e\u3068\u304d<br \/>\r\n\\[\r\n\\beta = \\alpha^3 = \\dfrac{1 \\pm i}{\\sqrt{2}}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, [2] \u3088\u308a\r\n\\[\r\na = \\pm \\sqrt{2} i , \\ \\beta = -1\r\n\\]\r\n\u3053\u308c\u306f, \u6761\u4ef6 (\u30ed) \u3092\u6e80\u305f\u3059.<\/p><\/li>\r\n<\/ul><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b \\(f(x)\\) \u306f\r\n\\[\\begin{align}\r\nf(x) & = \\underline{x^2 -\\dfrac{1 \\pm \\sqrt{3} i}{2} x -\\dfrac{1 \\mp \\sqrt{3} i}{2} , } \\\\\r\n& \\qquad \\underline{x^2 +\\dfrac{1 \\pm \\sqrt{3} i}{2} x -\\dfrac{1 \\mp \\sqrt{3} i}{2} ,} \\\\\r\n& \\qquad \\quad \\underline{x^2 \\pm \\sqrt{2} i x -1 \\quad ( \\ \\text{\u540c\u5f0f\u5185\u306f\u8907\u53f7\u540c\u9806} \\ )}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u8907\u7d20\u6570\u3092\u4fc2\u6570\u3068\u3059\u308b \\(2\\) \u6b21\u5f0f \\(f(x) = x^2 +ax +b\\) \u306b\u5bfe\u3057, \u6b21\u306e\u6761\u4ef6\u3092\u8003\u3048\u308b. (\u30a4)\u3000\\(f( x^3 )\\) \u306f \\(f(x)\\) \u3067\u5272\u308a\u5207\u308c\u308b. (\u30ed)\u3000\\(f(x)\\) \u306e\u4fc2\u6570 \\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201606\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[151],"tags":[140,162],"class_list":["post-1391","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2016","tag-kyoto_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1391","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=1391"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1391\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}