{"id":368,"date":"2012-04-13T01:34:01","date_gmt":"2012-04-12T16:34:01","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=368"},"modified":"2021-03-23T17:42:43","modified_gmt":"2021-03-23T08:42:43","slug":"kyr201204","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201204\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2012\uff1a\u7b2c4\u554f"},"content":{"rendered":"<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(\\sqrt[3]{2}\\) \u304c\u7121\u7406\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u305b\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(P(x)\\) \u306f\u6709\u7406\u6570\u3092\u4fc2\u6570\u3068\u3059\u308b \\(x\\) \u306e\u591a\u9805\u5f0f\u3067, \\(P( \\sqrt[3]{2} ) =0\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d \\(P(x)\\) \u306f \\(x^3-2\\) \u3067\u5272\u308a\u5207\u308c\u308b\u3053\u3068\u3092\u8a3c\u660e\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(\\sqrt[3]{2}\\) \u306f\u6709\u7406\u6570\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068, \u4e92\u3044\u306b\u7d20\u306a\u81ea\u7136\u6570 \\(m\\) , \\(n\\) \u3092\u7528\u3044\u3066 \\(\\sqrt[3]{2} =\\dfrac{m}{n} \\quad ... [1]\\) \u3068\u8868\u305b\u308b.<br \/>\r\n[1] \u3088\u308a\r\n\\[\r\n2 n^3 =m^3 \\quad ... [2]\r\n\\]\r\n\\(m\\) \u3068 \\(n\\) \u306f\u4e92\u3044\u306b\u7d20\u306a\u306e\u3067, \\(m\\) \u306f\u5076\u6570\u3067\u3042\u308a, \\(m =2 m'\\) \uff08 \\(m'\\) \u306f\u81ea\u7136\u6570\uff09\u3068\u304a\u3051\u308b.<br \/>\r\n\u3053\u308c\u3092 [2] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n2 n^3 & =8 {m'}^3 \\\\\r\n\\text{\u2234} \\quad n^3 & =4 {m'}^3\r\n\\end{align}\\]\r\n\\(m\\) \u3068 \\(n\\) \u306f\u4e92\u3044\u306b\u7d20\u306a\u306e\u3067, \\(n\\) \u3082\u5076\u6570\u3068\u306a\u308b\u304c, \u3053\u308c\u306f \\(m\\) \u3068 \\(n\\) \u304c \\(2\\) \u3092\u516c\u7d04\u6570\u306b\u3082\u3064\u3053\u3068\u306b\u306a\u308b\u306e\u3067, \u77db\u76fe\u3057\u3066\u3044\u308b.<br \/>\r\n\u3088\u3063\u3066, \\(\\sqrt[3]{2}\\) \u306f\u7121\u7406\u6570\u3067\u3042\u308b.<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(P(x)\\) \u3092 \\(x^3-2\\) \u3067\u5272\u3063\u305f\u5546\u3092 \\(Q(x)\\) , \u4f59\u308a\u3092 \\(ax^2+bx+c\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nP(x) = (x^3-2) Q(x) +ax+bx+c\r\n\\]\r\n\u3068\u8868\u305b\u308b.<br \/>\r\n\u6761\u4ef6\u3088\u308a, \u300c \\(a , b , c\\) \u306f\u3059\u3079\u3066\u6709\u7406\u6570\u300d ... [3] \u3067\u3042\u308b.<br \/>\r\n\\(x =\\sqrt[3]{2}\\) \u3092\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\r\n\\sqrt[3]{4} a +\\sqrt[3]{2} b +c =0 \\quad ... [4]\r\n\\]\r\n\u4e21\u8fba\u306b \\(\\sqrt[3]{2}\\) \u3092\u639b\u3051\u308b\u3068\r\n\\[\r\n2a +\\sqrt[3]{4} b +\\sqrt[3]{2} c =0 \\quad ... [5]\r\n\\]\r\n\\(\\text{[4]} \\times b -\\text{[5]} \\times a\\) \u3088\u308a\r\n\\[\r\n\\left( b^2 -ac \\right) \\sqrt[3]{2} +bc -2a^2 =0 \\quad ... [6]\r\n\\]\r\n\\(b^2 -ac \\neq 0\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\r\n\\sqrt[3]{2} =\\dfrac{2a^2-bc}{b^2 -ac}\r\n\\]\r\n\u3068\u306a\u308b\u304c, [3] \u3088\u308a\u53f3\u8fba\u306f\u6709\u7406\u6570\u306a\u306e\u3067, \u77db\u76fe\u3059\u308b.<br \/>\r\n\u3086\u3048\u306b\r\n\\[\r\nb^2 -ac = 0 \\quad ...[7]\r\n\\]\r\n\u3055\u3089\u306b [6] \u3088\u308a\r\n\\[\r\nbc -2a^2 =0 \\quad ...[8]\r\n\\]\r\n\\(\\text{[7]} \\times b +\\text{[8]} \\times a\\) \u3088\u308a\r\n\\[\r\nb^3 -2a^3 =0\r\n\\]\r\n\\(a \\neq 0\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\left( \\dfrac{b}{a} \\right)^3 & =2 \\\\\r\n\\text{\u2234} \\quad \\dfrac{b}{a} & = \\sqrt[3]{2}\r\n\\end{align}\\]\r\n[3] \u3088\u308a\u5de6\u8fba\u306f\u6709\u7406\u6570\u306a\u306e\u3067, \u77db\u76fe\u3059\u308b.<br \/>\r\n\u3086\u3048\u306b\r\n\\[\r\na=0\r\n\\]\r\n[7] \u306b\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\r\nb=0\r\n\\]\r\n[4] \u306b\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\r\nc=0\r\n\\]\r\n\u3088\u3063\u3066, \u4f59\u308a\u304c \\(0\\) \u306b\u306a\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"(1)\u3000\\(\\sqrt[3]{2}\\) \u304c\u7121\u7406\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u305b\u3088. (2)\u3000\\(P(x)\\) \u306f\u6709\u7406\u6570\u3092\u4fc2\u6570\u3068\u3059\u308b \\(x\\) \u306e\u591a\u9805\u5f0f\u3067, \\(P( \\sqrt[3]{2} ) =0\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3059\u308b. \u3053 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201204\/\">\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":[59],"tags":[140,68],"class_list":["post-368","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2012","tag-kyoto_r","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/368","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=368"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/368\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}