{"id":479,"date":"2012-11-24T14:41:38","date_gmt":"2012-11-24T05:41:38","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=479"},"modified":"2021-09-23T21:10:52","modified_gmt":"2021-09-23T12:10:52","slug":"thr201101","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201101\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2011\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \u4e0d\u7b49\u5f0f\r\n\\[\r\ny \\leqq 2ax -a^2 +2a +2\r\n\\]\r\n\u306e\u8868\u3059\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u9818\u57df\u3092 \\(D(a)\\) \u3068\u304a\u304f.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(-1 \\leqq a \\leqq 2\\) \u3092\u6e80\u305f\u3059\u3059\u3079\u3066\u306e \\(a\\) \u306b\u5bfe\u3057 \\(D(a)\\) \u306e\u70b9\u3068\u306a\u308b\u3088\u3046\u306a\u70b9 \\((p,q)\\) \u306e\u7bc4\u56f2\u3092\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(-1 \\leqq a \\leqq 2\\) \u3092\u6e80\u305f\u3059\u3044\u305a\u308c\u304b\u306e \\(a\\) \u306b\u5bfe\u3057 \\(D(a)\\) \u306e\u70b9\u3068\u306a\u308b\u3088\u3046\u306a\u70b9 \\((p,q)\\) \u306e\u7bc4\u56f2\u3092\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong>\r\n\\[\r\ny \\leqq 2ax -a^2 +2a +2 \\quad ... [1] \\ .\r\n\\]\r\n\u70b9 \\((p,q)\\) \u304c [1] \u3092\u307f\u305f\u3059\u3068\u304d\r\n\\[\r\na^2 -2(p+1)a +q -2 \\leqq 0 \\quad ... [2] \\ .\r\n\\]\r\n[2] \u306e\u53f3\u8fba\u3092 \\(a\\) \u306e\u95a2\u6570\u3068\u307f\u306a\u3057\u3066, \\(f(a)\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nf(a) = \\{ a-(p+1) \\}^2 +q -p^2 -2p -3 \\ .\r\n\\]\r\n\u3053\u308c\u306f\u4e0b\u306b\u51f8\u306e \\(2\\) \u6b21\u95a2\u6570\u3067\u3042\u308b.
    \r\n[2] \u304c \\(-1 \\leqq a \\leqq 2\\) \u306b\u304a\u3044\u3066\u5e38\u306b\u6210\u7acb\u3059\u308b\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\nf(-1) \\leqq 0 \\ & \\text{\u304b\u3064} \\ f(2) \\leqq 0 \\\\\r\n2p+q+1 \\leqq 0 \\ & \\text{\u304b\u3064} \\ -4p+q-2 \\leqq 0 \\\\\r\n\\text{\u2234} \\quad q \\leqq -2p-1 \\ & \\text{\u304b\u3064} \\ q \\leqq 4p+2 \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u9818\u57df\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09.<\/p>\r\n\"\"\r\n

    (2)<\/strong><\/p>\r\n[2] \u304c \\(-1 \\leqq a \\leqq 2\\) \u306e\u3044\u305a\u308c\u304b\u3067\u6210\u7acb\u3059\u308b\u6761\u4ef6\u306f<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(f(-1) \\leqq 0\\) \u307e\u305f\u306f \\(f(2) \\leqq 0\\)<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(f(-1) \\gt 0\\) , \\(f(2) \\gt 0\\) , \\(f(p+1) \\leqq 0\\) , \\(-1 \\leqq p+1 \\leqq 2\\)<\/p><\/li>\r\n<\/ol>\r\n

      \u306e\u3044\u305a\u308c\u304b\u3067\u3042\u308b.<\/p>\r\n

        \r\n

      1. 1*<\/strong> \u306e\u3068\u304d
        \r\n(1)<\/strong> \u306e\u9014\u4e2d\u7d4c\u904e\u3088\u308a\r\n\\[\r\nq \\leqq -2p-1 \\ \\text{\u307e\u305f\u306f} \\ q \\leqq 4p+2 \\ .\r\n\\]<\/li>\r\n

      2. 2*<\/strong>\u306e\u3068\u304d\r\n\\[\r\nq \\gt -2p-1 , \\ q \\gt 4p+2 , \\ q \\leqq p^2 +2p +3 , \\ -2 \\leqq p \\leqq 1 \\ .\r\n\\]<\/li>\r\n<\/ol>\r\n

        \u3088\u3063\u3066, \u6c42\u3081\u308b\u9818\u57df\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09.<\/p>\r\n\"\"\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \u4e0d\u7b49\u5f0f \\[ y \\leqq 2ax -a^2 +2a +2 \\] \u306e\u8868\u3059\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u9818\u57df\u3092 \\(D(a)\\) \u3068\u304a\u304f. (1)\u3000\\(-1 \\leqq a \\leqq 2\\) \u3092\u6e80\u305f\u3059\u3059\u3079\u3066\u306e … \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":[73],"tags":[148,13],"class_list":["post-479","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2011","tag-tohoku_r","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/479","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=479"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/479\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=479"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=479"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}