{"id":1312,"date":"2015-10-19T00:51:52","date_gmt":"2015-10-18T15:51:52","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1312"},"modified":"2021-10-20T13:31:21","modified_gmt":"2021-10-20T04:31:21","slug":"ykr201503","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201503\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2015\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \\(xy\\) \u5e73\u9762\u4e0a\u306e\u653e\u7269\u7dda \\(C : \\ y = (x-a)^2 -2a^2 +1\\) \u3092\u8003\u3048\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(a\\) \u304c\u3059\u3079\u3066\u306e\u5b9f\u6570\u3092\u52d5\u304f\u3068\u304d, \\(C\\) \u304c\u901a\u904e\u3059\u308b\u9818\u57df\u3092\u6c42\u3081, \u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a\\) \u304c \\(-1 \\leqq a \\leqq 1\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d, \\(C\\) \u304c\u901a\u904e\u3059\u308b\u9818\u57df\u3092\u6c42\u3081, \u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(C\\) \u306e\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\na^2 +2xa +y -x^2 -1 = 0\r\n\\]\r\n\u3053\u306e \\(a\\) \u306e \\(2\\) \u6b21\u65b9\u7a0b\u5f0f\u304c\u5b9f\u6570\u89e3\u3092\u3082\u3064\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u306e\u3067, \u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{D}{4} & = x^2 -( y -x^2 -1 ) \\geqq 0 \\\\\r\n\\text{\u2234} \\quad & y \\leqq 2x^2 +1\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\"ykr20150301\"\r\n

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

    \\(C\\) \u306e\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\\begin{align}\r\ny & = -a^2 -2xa +x^2 +1 \\\\\r\n& = -(a+x)^2 +2x^2 +1\r\n\\end{align}\\]\r\n\u3053\u308c\u3092 \\(a\\) \u306e\u95a2\u6570\u3068\u307f\u306a\u3057\u3066 \\(f(a)\\) \u3068\u304a\u304f.
    \r\n\\(x = k\\) \u306b\u304a\u3051\u308b \\(f(a)\\) \u306e\u6700\u5927\u5024, \u6700\u5c0f\u5024\u3092\u305d\u308c\u305e\u308c \\(M(a) , m(a)\\) \u3068\u304a\u304f\u3068, \u6c42\u3081\u308b\u9818\u57df\u306f\r\n\\[\r\nm(a) \\leqq y \\leqq M(a)\r\n\\]\r\n\u3068\u8868\u305b\u308b.
    \r\n\\(-1 \\leqq a \\leqq 1\\) \u306b\u6ce8\u610f\u3059\u308c\u3070, \\(M(a) , m(a)\\) \u306e\u5019\u88dc\u306f\r\n\\[\\begin{align}\r\nf(-1) & = x^2 +2x , \\quad f(1) = x^2 -2x , \\\\\r\nf( -a ) & = 2x^2 +1 \\ \\left( -1 \\leqq a \\leqq 1 \\ \\text{\u306e\u3068\u304d} , M(a) \\ \\text{\u306e\u307f} \\right)\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308c\u3070, \u6c42\u3081\u308b\u9818\u57df\u306f\r\n\\[\r\n\\left\\{ \\begin{array}{ll} x^2 +2x \\leqq y \\leqq x^2 -2x & ( \\ x \\leqq -1 \\ \\text{\u306e\u3068\u304d} ) \\\\ x^2 +2x \\leqq y \\leqq 2 x^2 +1 & ( \\ -1 \\lt x \\leqq 0 \\ \\text{\u306e\u3068\u304d} ) \\\\ x^2 -2x \\leqq y \\leqq 2 x^2 +1 & ( \\ 0 \\lt x \\leqq 1 \\ \\text{\u306e\u3068\u304d} ) \\\\ x^2 -2x \\leqq y \\leqq x^2 +2x & ( \\ x \\gt 1 \\ \\text{\u306e\u3068\u304d} ) \\end{array} \\right.\r\n\\]\r\n\u3067\u3042\u308a, \u56f3\u793a\u3059\u308c\u3070\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09.<\/p>\r\n\"ykr20150302\"\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \\(xy\\) \u5e73\u9762\u4e0a\u306e\u653e\u7269\u7dda \\(C : \\ y = (x-a)^2 -2a^2 +1\\) \u3092\u8003\u3048\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(a\\) \u304c\u3059\u3079\u3066\u306e\u5b9f\u6570\u3092\u52d5\u304f\u3068\u304d, \\(C\\) \u304c\u901a\u904e\u3059 … \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":[133],"tags":[137,9],"class_list":["post-1312","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2015","tag-137","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1312","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=1312"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1312\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}