{"id":2050,"date":"2021-12-22T06:33:05","date_gmt":"2021-12-21T21:33:05","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2050"},"modified":"2024-04-10T07:50:22","modified_gmt":"2024-04-09T22:50:22","slug":"htb202103","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb202103\/","title":{"rendered":"\u4e00\u6a4b\u59272021\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\r\n<p>\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(a , b\\) \u3092\u5b9f\u6570\u3068\u3057, \\(2\\) \u6b21\u65b9\u7a0b\u5f0f \\(x^2 -ax +b = 0\\) \u304c\u5b9f\u6570\u89e3 \\(\\alpha , \\beta\\) \u3092\u3082\u3064\u3068\u3059\u308b.\r\n\u305f\u3060\u3057, \u91cd\u89e3\u306e\u5834\u5408\u306f \\(\\alpha = \\beta\\) \u3068\u3059\u308b.\r\n\\(3\\) \u8fba\u306e\u9577\u3055\u304c \\(1 , \\alpha , \\beta\\) \u3067\u3042\u308b\u4e09\u89d2\u5f62\u304c\u5b58\u5728\u3059\u308b \\(( a , b )\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(3\\) \u8fba\u306e\u9577\u3055\u304c \\(1 , \\alpha , \\beta\\) \u3067\u3042\u308b\u4e09\u89d2\u5f62\u304c\u5b58\u5728\u3059\u308b\u3068\u304d,\r\n\\[\r\n\\dfrac{\\alpha \\beta +1}{( \\alpha +\\beta )^2}\r\n\\]\r\n\u306e\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\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>\\(2\\) \u6b21\u65b9\u7a0b\u5f0f\u306e\u5224\u5225\u5f0f\u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\nD & = a^2 -4b \\geqq 0 \\\\\r\n\\text{\u2234} \\quad & b \\leqq \\dfrac{a^2}{4} \\quad ... [1]\r\n\\end{align}\\]\r\n\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\n\\alpha +\\beta = a \\ , \\ \\alpha \\beta = b \\quad ... [2]\r\n\\]\r\n\\(\\alpha \\lt \\beta\\) \u3068\u3057\u3066\u3082\u4e00\u822c\u6027\u3092\u5931\u308f\u306a\u3044.<br \/>\r\n\u4e09\u89d2\u5f62\u304c\u5b58\u5728\u3059\u308b\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\n\\alpha +\\beta \\gt 1 \\ & \\text{\u304b\u3064} \\ \\alpha +1 \\lt \\beta \\\\\r\n\\text{\u2234} \\quad a \\gt 1 \\ & \\text{\u304b\u3064} \\ \\beta -\\alpha \\lt 1 \\quad ... [3]\r\n\\end{align}\\]\r\n[2] \u3088\u308a\r\n\\[\\begin{align}\r\n\\beta -\\alpha & = \\sqrt{( \\alpha +\\beta )^2 -4 \\alpha \\beta} \\\\\r\n& = \\sqrt{a^2 -4b}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\na^2 -4b & \\lt 1 \\\\\r\n\\text{\u2234} \\quad b & \\gt \\dfrac{a^2}{4} -\\dfrac{1}{4} \\quad ... [4]\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, [1] [3] [4] \u3088\u308a, \u6c42\u3081\u308b \\(( a , b )\\) \u306e\u7bc4\u56f2\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5b9f\u7dda\u5883\u754c\u3092\u542b\u307f, \u70b9\u7dda\u5883\u754c\u3068\u25cb\u306f\u542b\u307e\u306a\u3044. \uff09<\/p>\r\n<img decoding=\"async\" src=\"\/nyushi\/wp-content\/uploads\/htb20210301.svg\" alt=\"htb20210301\" class=\"aligncenter size-full\" \/>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(k = \\dfrac{\\alpha \\beta +1}{( \\alpha +\\beta )^2}\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nk & = \\dfrac{b+1}{a^2} \\\\\r\n\\text{\u2234} \\quad b & = k a^2 -1 \\quad ... [5]\r\n\\end{align}\\]\r\n[5] \u306f, \u70b9 \\(( 0 , -1 )\\) \u3092\u9802\u70b9\u306b\u3082\u3064\u653e\u7269\u7dda\u307e\u305f\u306f\u76f4\u7dda : \\(b = -1\\) \u3092\u8868\u3059.<br \/>\r\n[5] \u304c <strong>(1)<\/strong> \u3067\u6c42\u3081\u305f\u9818\u57df\u3068\u5171\u6709\u70b9\u3092 \\(k\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.<\/p>\r\n<ol>\r\n<li><p><strong>1&#42;<\/strong>\u3000\\(k \\leqq 0\\) \u306e\u3068\u304d<br \/>\r\n[5] \u306f\u5171\u6709\u70b9\u3092\u3082\u305f\u306a\u3044.<\/p><\/li>\r\n<li><p><strong>2&#42;<\/strong>\u3000\\(k \\gt 0\\) \u306e\u3068\u304d<br \/>\r\n[5] \u304c, \u5883\u754c\u3068\u306a\u3063\u3066\u3044\u308b\u653e\u7269\u7dda\u3068\u4ea4\u308f\u308b\u6761\u4ef6\u306f\r\n\\[\r\na \\gt \\dfrac{1}{4} \\quad ... [6]\r\n\\]\r\n\u70b9 \\(\\left( 1 , \\dfrac{1}{4} \\right)\\) \u3092\u901a\u308b\u306e\u306f\r\n\\[\\begin{align}\r\n\\dfrac{1}{4} & = k -1 \\\\\r\n\\text{\u2234} \\quad k & = \\dfrac{5}{4}\r\n\\end{align}\\]\r\n\u3086\u3048\u306b, \u5171\u6709\u70b9\u3092\u3082\u3064\u6761\u4ef6\u306f\r\n\\[\r\n\\dfrac{1}{4} \\lt k \\lt \\dfrac{5}{4}\r\n\\]<\/li>\r\n<\/ol>\r\n<p>\u3088\u3063\u3066, \u6c42\u3081\u308b\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{\\dfrac{1}{4} \\lt \\dfrac{\\alpha \\beta +1}{( \\alpha +\\beta )^2} \\lt \\dfrac{5}{4}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(a , b\\) \u3092\u5b9f\u6570\u3068\u3057, \\(2\\) \u6b21\u65b9\u7a0b\u5f0f \\(x^2 -ax +b = 0\\) \u304c\u5b9f\u6570\u89e3 \\(\\alpha , \\beta\\) \u3092\u3082\u3064\u3068\u3059\u308b. \u305f\u3060\u3057, \u91cd\u89e3\u306e\u5834\u5408\u306f \\(\\al &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/htb202103\/\">\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":[181],"tags":[146,165],"class_list":["post-2050","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2021","tag-hitotsubashi","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2050","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=2050"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2050\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}