{"id":912,"date":"2013-08-31T08:47:28","date_gmt":"2013-08-30T23:47:28","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=912"},"modified":"2021-09-29T23:57:54","modified_gmt":"2021-09-29T14:57:54","slug":"kbr201301","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr201301\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2013\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(f(x) , g(t)\\) \u3092\r\n\\[\\begin{align}\r\nf(x) & = x^3-x^2-2x+1 \\\\\r\ng(t) & = \\cos 3t -\\cos 2t +\\cos t\r\n\\end{align}\\]\r\n\u3068\u304a\u304f.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(2 g(t) -1 = f( 2 \\cos t )\\) \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\theta = \\dfrac{\\pi}{7}\\) \u306e\u3068\u304d, \\(2 g( \\theta ) \\cos \\theta = 1 +\\cos \\theta -2 g( \\theta )\\) \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(2 \\cos \\dfrac{\\pi}{7}\\) \u306f \\(3\\) \u6b21\u65b9\u7a0b\u5f0f \\(f(x) = 0\\) \u306e\u89e3\u3067\u3042\u308b\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

    \\(2\\) \u500d\u89d2, \\(3\\) \u500d\u89d2\u306e\u516c\u5f0f\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n2 g(t) -1 & = 2 ( 4 \\cos^3 t -3 \\cos t ) \\\\\r\n& \\qquad -2 ( 2 \\cos^2 -1 ) +2 \\cos t -1 \\\\\r\n& = ( 2 \\cos t )^3 -( 2 \\cos t )^2 -2 ( 2 \\cos t ) +1 \\\\\r\n& = f ( 2 \\cos t )\r\n\\end{align}\\]\r\n

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

    \\(\\theta = \\dfrac{\\pi}{7}\\) \u306e\u3068\u304d,\r\n\\[\r\n\\cos 4 \\theta = \\cos ( \\pi -3\\theta ) = -\\cos 3 \\theta\r\n\\]\r\n\u3053\u308c\u3068, \u534a\u89d2\u306e\u516c\u5f0f, \u7a4d\u548c\u5909\u63db\u306e\u516c\u5f0f\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n2 g( \\theta ) & \\cos \\theta \\\\\r\n& = 2 \\cos 3 \\theta \\cos \\theta -2 \\cos 2 \\theta \\cos \\theta +2 \\cos^2 \\theta \\\\\r\n& = \\cos 4 \\theta +\\cos 2 \\theta -\\cos 3 \\theta -\\cos \\theta +\\cos 2 \\theta +1 \\\\\r\n& = -2 \\cos 3 \\theta +2 \\cos 2 \\theta -\\cos \\theta +1 \\\\\r\n& = 1 +\\cos \\theta -2 ( \\cos 3 \\theta -2 \\cos 2 \\theta +\\cos \\theta ) \\\\\r\n& = 1 +\\cos \\theta -2 g( \\theta )\r\n\\end{align}\\]\r\n

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

    (2)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\n\\left( \\cos \\dfrac{\\pi}{7} +1 \\right) \\left( 2g \\left( \\dfrac{\\pi}{7} \\right) -1 \\right) = 0\r\n\\]\r\n\\(\\cos \\dfrac{\\pi}{7} \\neq 1\\) \u306a\u306e\u3067\r\n\\[\r\n2g \\left( \\dfrac{\\pi}{7} \\right) -1 = 0 \\quad ... [1]\r\n\\]\r\n(1)<\/strong> \u306e\u7d50\u679c\u306b \\(t = \\dfrac{\\pi}{7}\\) \u3092\u4ee3\u5165\u3057\u3066, [1] \u3092\u7528\u3044\u308c\u3070\r\n\\[\r\nf \\left( 2 \\cos \\dfrac{\\pi}{7} \\right) = 2g \\left( \\dfrac{\\pi}{7} \\right) -1 = 0\r\n\\]\r\n\u3088\u3063\u3066, \\(x = \\cos \\dfrac{\\pi}{7}\\) \u306f \\(f(x) = 0\\) \u306e\u89e3\u3067\u3042\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(f(x) , g(t)\\) \u3092 \\[\\begin{align} f(x) & = x^3-x^2-2x+1 \\\\ g(t) & = \\cos 3t -\\cos 2t +\\cos t \\end{align}\\] \u3068\u304a\u304f … \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":[102],"tags":[144,111],"class_list":["post-912","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2013","tag-tsukuba_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/912","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=912"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/912\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=912"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=912"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}