{"id":110,"date":"2011-11-27T19:21:47","date_gmt":"2011-11-27T10:21:47","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=110"},"modified":"2021-03-23T19:14:31","modified_gmt":"2021-03-23T10:14:31","slug":"kyr201002","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201002\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592010\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(x\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b. \u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(3\\) \u70b9A \\(( 0 , 1 )\\) , B \\(( 0 , 2 )\\) , P \\(( x , x )\\) \u3092\u3068\u308a, \u25b3APB\u3092\u8003\u3048\u308b.\r\n\\(x\\) \u306e\u5024\u304c\u5909\u5316\u3059\u308b\u3068\u304d, \\(\\angle \\text{APB}\\) \u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\\(\\angle \\text{APB} = \\theta\\) \u3068\u304a\u304f.<br \/>\r\n\u76f4\u7dda AP, BP \u304c \\(x\\) \u8ef8\u6b63\u65b9\u5411\u3068\u306a\u3059\u89d2\u3092 \\(\\theta _ 1 , \\theta _ 2\\) \u3068\u304a\u304f\u3068,\r\n\\[\r\n\\tan \\theta _ 1 = \\dfrac{x-1}{x} , \\quad \\tan \\theta _ 2 = \\dfrac{x-2}{x}\r\n\\]\r\n\\(x \\gt 0\\) \u306a\u306e\u3067\r\n\\[\r\n-\\dfrac{\\pi}{2} \\lt \\theta _ 1 \\lt \\theta _ 2 \\lt \\dfrac{\\pi}{4}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(\\theta = \\theta _ 1 -\\theta _ 2\\) \u3068\u8868\u305b\u308b.\r\n\\[\\begin{align}\r\n\\tan \\theta & = \\tan ( \\theta _ 1 -\\theta _ 2 ) = \\dfrac{\\dfrac{x-1}{x} -\\dfrac{x-2}{x}}{1 +\\dfrac{x-1}{x} \\cdot \\dfrac{x-2}{x}} \\\\\r\n& = \\dfrac{x}{x^2 +(x-2)(x-1)} = \\dfrac{x}{2x^2 -3x +2} \\\\\r\n& = \\dfrac{1}{2 \\left( x +\\dfrac{1}{x} \\right) -3} \\quad ... [ \\text{A} ]\r\n\\end{align}\\]\r\n\u3053\u3053\u3067 \\(x \\gt 0\\) \u306a\u306e\u3067\u76f8\u52a0\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\nx +\\dfrac{1}{x} \\leqq 2 \\sqrt{x \\cdot \\dfrac{1}{x}} = 2\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f\r\n\\[\\begin{align}\r\nx & = \\dfrac{1}{x} \\\\\r\n\\text{\u2234} \\quad x & = 1\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u7528\u3044\u308b\u3068,\r\n\\[\r\n[ \\text{A} ] \\geqq \\dfrac{1}{2 \\cdot 2 -3} = 1\r\n\\]\r\n\u3053\u306e\u3068\u304d\r\n\\[\r\n\\theta = \\dfrac{\\pi}{4}\r\n\\]\r\n\u3086\u3048\u306b \\( x = 1\\) \u306e\u3068\u304d, \\(\\angle \\text{APB}\\) \u306f\u6700\u5927\u5024 \\(\\underline{45^{\\circ}}\\) \u3092\u3068\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(x\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b. \u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(3\\) \u70b9A \\(( 0 , 1 )\\) , B \\(( 0 , 2 )\\) , P \\(( x , x )\\) \u3092\u3068\u308a, \u25b3APB\u3092\u8003\u3048\u308b. \\(x\\) \u306e\u5024\u304c\u5909\u5316\u3059\u308b &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201002\/\">\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":[22],"tags":[140,14],"class_list":["post-110","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2010","tag-kyoto_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/110","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=110"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/110\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}