{"id":1287,"date":"2015-09-23T00:18:00","date_gmt":"2015-09-22T15:18:00","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1287"},"modified":"2021-09-16T09:46:16","modified_gmt":"2021-09-16T00:46:16","slug":"thr201503","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201503\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2015\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u30b5\u30a4\u30b3\u30ed\u3092 \\(3\\) \u56de\u6295\u3052\u3066\u51fa\u305f\u76ee\u306e\u6570\u3092\u9806\u306b \\(p _ 1 , p _ 2 \\ p _ 3\\) \u3068\u3057, \\(x\\) \u306e \\(2\\) \u6b21\u65b9\u7a0b\u5f0f\r\n\\[\r\n2 p _ 1 x^2 +p _ 2 x +2p _ 3 = 0 \\quad ... \\text{(\uff0a)}\r\n\\]\r\n\u3092\u8003\u3048\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u65b9\u7a0b\u5f0f (\uff0a) \u304c\u5b9f\u6570\u89e3\u3092\u3082\u3064\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u65b9\u7a0b\u5f0f (\uff0a) \u304c\u5b9f\u6570\u3067\u306a\u3044 \\(2\\) \u3064\u306e\u8907\u7d20\u6570\u89e3 \\(\\alpha , \\beta\\) \u3092\u3082\u3061, \u304b\u3064 \\(\\alpha \\beta = 1\\) \u304c\u6210\u308a\u7acb\u3064\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u65b9\u7a0b\u5f0f (\uff0a) \u304c\u5b9f\u6570\u3067\u306a\u3044 \\(2\\) \u3064\u306e\u8907\u7d20\u6570\u89e3 \\(\\alpha , \\beta\\) \u3092\u3082\u3061, \u304b\u3064 \\(\\alpha \\beta \\lt 1\\) \u304c\u6210\u308a\u7acb\u3064\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

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

    (\uff0a) \u306e\u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\nD = {p _ 2}^2 & -16 p _ 1 p _ 3 \\geqq 0 \\\\\r\n\\text{\u2234} \\quad & {p _ 2}^2 \\geqq 16 p _ 1 p _ 3 \\ .\r\n\\end{align}\\]\r\n\\(p _ 1 , p _ 2 , p _ 3\\) \u306f\u30b5\u30a4\u30b3\u30ed\u306e\u76ee\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n16 p _ 1 p _ 3 \\leqq {p _ 2}^2 & \\leqq 6^2 \\\\\r\np _ 1 p _ 3 & \\leqq \\dfrac{9}{4} \\\\\r\n\\text{\u2234} \\quad p _ 1 p _ 3 & = 1 , 2 \\ .\r\n\\end{align}\\]\r\n\u305d\u308c\u305e\u308c\u306e\u5834\u5408\u306b\u3064\u3044\u3066<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(p _ 1 p _ 3 = 1\\) \u306e\u3068\u304d, \\(p^2 \\geqq 16\\) \u306a\u306e\u3067\r\n\\[\r\np _ 2 = 4 , 5 , 6 \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(( p _ 1 , p _ 2 , p _ 3 )\\) \u306e\u7d44\u306f, \\(3\\) \u901a\u308a.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(p _ 1 p _ 3 = 2\\) \u306e\u3068\u304d, \\(p^2 \\geqq 32\\) \u306a\u306e\u3067\r\n\\[\r\np _ 2 = 6 \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(( p _ 1 , p _ 2 , p _ 3 )\\) \u306e\u7d44\u306f, \\(2\\) \u901a\u308a.<\/p><\/li>\r\n<\/ol>\r\n

      \u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{3+2}{6^3} = \\underline{\\dfrac{5}{216}} \\ .\r\n\\]\r\n

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

      \u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\n\\alpha \\beta = \\dfrac{p _ 3}{p _ 1} \\ .\r\n\\]\r\n\u306a\u306e\u3067, \\(\\alpha \\beta = 1\\) \u3088\u308a\r\n\\[\r\np _ 1 = p _ 3 \\quad ... [1] \\ .\r\n\\]\r\n[1] \u3092\u307f\u305f\u3059 \\(( p _ 1 , p _ 2 , p _ 3 )\\) \u306e\u7d44\u306f\r\n\\[\r\n6 \\cdot 6 = 36 \\ \\text{\u901a\u308a} \\ .\r\n\\]\r\n\u3053\u306e\u3046\u3061, (1)<\/strong> \u306e1*<\/strong> \u306e\u5834\u5408\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308c\u3070, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{36 -3}{6^3} = \\underline{\\dfrac{11}{72}} \\ .\r\n\\]\r\n

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

      \\(\\alpha \\beta \\lt 1\\) \u3088\u308a\r\n\\[\r\np _ 1 \\gt p _ 3 \\quad ... [2] \\ .\r\n\\]\r\n[2] \u3092\u307f\u305f\u3059 \\(( p _ 1 , p _ 2 , p _ 3 )\\) \u306e\u7d44\u306f\r\n\\[\r\n{} _ {6} \\text{C} {} _ 2 \\cdot 6 = 90 \\ \\text{\u901a\u308a} \\ .\r\n\\]\r\n\u3053\u306e\u3046\u3061, (1)<\/strong> \u306e2*<\/strong> \u306e\u4e2d\u306e \\(1\\) \u901a\u308a\uff08 \\(( p _ 1 , p _ 2 , p _ 3 ) = ( 2 , 6 , 1 )\\) \uff09\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308c\u3070, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{90 -1}{6^3} = \\underline{\\dfrac{89}{216}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u30b5\u30a4\u30b3\u30ed\u3092 \\(3\\) \u56de\u6295\u3052\u3066\u51fa\u305f\u76ee\u306e\u6570\u3092\u9806\u306b \\(p _ 1 , p _ 2 \\ p _ 3\\) \u3068\u3057, \\(x\\) \u306e \\(2\\) \u6b21\u65b9\u7a0b\u5f0f \\[ 2 p _ 1 x^2 +p _ 2 x +2p _ 3 = 0 … \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":[131],"tags":[148,137],"class_list":["post-1287","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2015","tag-tohoku_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1287","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=1287"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1287\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}