{"id":1274,"date":"2015-09-11T10:16:53","date_gmt":"2015-09-11T01:16:53","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1274"},"modified":"2021-09-14T20:21:04","modified_gmt":"2021-09-14T11:21:04","slug":"ngr201502","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201502\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2015\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(a = \\sqrt{13} +\\sqrt{9 +2 \\sqrt{17}} +\\sqrt{9 -2 \\sqrt{17}}\\) \u3068\u3059\u308b\u3068\u304d, \u6574\u6570\u4fc2\u6570\u306e \\(4\\) \u6b21\u591a\u9805\u5f0f \\(f(x)\\) \u3067 \\(f(a) = 0\\) \u3068\u306a\u308b\u3082\u306e\u306e\u3046\u3061, \\(x^4\\) \u306e\u4fc2\u6570\u304c \\(1\\) \u3067\u3042\u308b\u3082\u306e\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(8\\) \u3064\u306e\u5b9f\u6570\r\n\\[\r\n\\pm \\sqrt{13} \\pm \\sqrt{9 +2 \\sqrt{17}} \\pm \\sqrt{9 -2 \\sqrt{17}}\r\n\\]\r\n\uff08\u305f\u3060\u3057, \u8907\u53f7 \\(\\pm\\) \u306f\u3059\u3079\u3066\u306e\u53ef\u80fd\u6027\u306b\u308f\u305f\u308b\uff09\u306e\u4e2d\u3067, (1)<\/strong> \u3067\u6c42\u3081\u305f \\(f(x)\\) \u306b\u5bfe\u3057\u3066\u65b9\u7a0b\u5f0f \\(f(x) = 0\\) \u306e\u89e3\u3068\u306a\u308b\u3082\u306e\u3092\u3059\u3079\u3066\u6c42\u3081, \u305d\u308c\u4ee5\u5916\u306e\u3082\u306e\u304c\u89e3\u3067\u306a\u3044\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000(2)<\/strong> \u3067\u6c42\u3081\u305f \\(f(x) = 0\\) \u306e\u89e3\u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u8abf\u3079, \u305d\u308c\u3089\u3092\u5927\u304d\u3044\u9806\u306b\u4e26\u3079\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u6761\u4ef6\u3088\u308a\r\n\\[\r\na -\\sqrt{13} = \\sqrt{9 +2 \\sqrt{17}} +\\sqrt{9 -2 \\sqrt{17}} \\quad ... [1] \\ .\r\n\\]\r\n\u3053\u308c\u3092\u4e21\u8fba\u5e73\u65b9\u3059\u308b\u3068\r\n\\[\\begin{align}\r\na^2 -2 \\sqrt{13} +13 & = 2 \\cdot 9 +2 \\sqrt{81 -68} \\\\\r\n\\text{\u2234} \\quad a^2 -5 & = 2 \\sqrt{13} (a+1) \\quad ... [2] \\ .\r\n\\end{align}\\]\r\n\u3055\u3089\u306b\u4e21\u8fba\u5e73\u65b9\u3057\u3066\r\n\\[\\begin{align}\r\na^4 -10a^2 +25 & = 52a^2 +104a +52 \\\\\r\n\\text{\u2234} \\quad a^4 -62a^2 & -104a -27 = 0 \\quad ... [3] \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u591a\u9805\u5f0f \\(f(x)\\) \u306f\r\n\\[\r\nf(x) = \\underline{x^4 -62x^2 -104x -27} \\ .\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n[2] \u3092\u5e73\u65b9\u3057\u3066 [3] \u3092\u5f97\u305f\u306e\u3067\r\n\\[\r\na^2 -5 = \\pm 2 \\sqrt{13} (a+1) \\ .\r\n\\]\r\n\u3082 [3] \u3092\u307f\u305f\u3059.
    \r\n\u3053\u308c\u3092\u5909\u5f62\u3057\u3066\r\n\\[\\begin{align}\r\na^2 \\mp 2 \\sqrt{13} a +13 & = 18 \\pm 2 \\sqrt{13} \\\\\r\n\\text{\u2234} \\quad ( a \\mp \\sqrt{13} )^2 & = \\left( \\sqrt{9 +2 \\sqrt{17}} \\pm \\sqrt{9 -2 \\sqrt{17}} \\right)^2 \\ .\r\n\\end{align}\\]\r\n[1] \u3092\u5e73\u65b9\u3057\u3066\u3053\u308c\u3092\u5f97\u305f\u306e\u3067\r\n\\[\\begin{align}\r\na \\mp \\sqrt{13} & = \\pm \\left( \\sqrt{9 +2 \\sqrt{17}} \\pm \\sqrt{9 -2 \\sqrt{17}} \\right) \\\\\r\n\\text{\u2234} \\quad a & = \\underline{\\pm} _ {[4]} \\sqrt{13} \\pm \\left( \\sqrt{9 +2 \\sqrt{17}} \\underline{\\pm} _ {[4]} \\sqrt{9 -2 \\sqrt{17}} \\right) \\ .\r\n\\end{align}\\]\r\n\u305f\u3060\u3057, \u4e0b\u7dda [4] \u306e\u8907\u53f7\u306f\u540c\u9806.
    \r\n\u3088\u3063\u3066, \\(f(x) = 0\\) \u306e\u89e3\u306f\r\n\\[\\begin{align}\r\nx & = \\underline{\\sqrt{13} \\pm \\sqrt{9 +2 \\sqrt{17}} \\pm \\sqrt{9 -2 \\sqrt{17}} , } \\\\\r\n& \\qquad \\underline{-\\sqrt{13} \\pm \\sqrt{9 +2 \\sqrt{17}} \\mp \\sqrt{9 -2 \\sqrt{17}} \\quad ( \\text{\u8907\u53f7\u540c\u9806} ) \\quad} \\ .\r\n\\end{align}\\]\r\n\\(4\\) \u6b21\u65b9\u7a0b\u5f0f\u306f\u9ad8\u3005 \\(4\\) \u500b\u306e\u89e3\u3057\u304b\u3082\u305f\u306a\u3044\u306e\u3067, \u3053\u308c\u4ee5\u5916\u306b\u89e3\u306f\u306a\u3044.<\/p>\r\n

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

    \\(4 \\lt \\sqrt{17} \\lt \\dfrac{9}{2}\\) \u306a\u306e\u3067\r\n\\[\r\n0 \\lt 9 -2 \\sqrt{17} \\lt 1 , \\ 17 \\lt 9 +2 \\sqrt{17} \\lt 18 \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\n\\sqrt{9 -2 \\sqrt{17}} \\lt \\sqrt{13} \\lt \\sqrt{9 +2 \\sqrt{17}} \\ .\r\n\\]\r\n\u3053\u308c\u3092\u7528\u3044\u3066\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n& \\underline{\\sqrt{13} +\\sqrt{9 +2 \\sqrt{17}} +\\sqrt{9 -2 \\sqrt{17}}} \\\\\r\n& \\quad \\underline{\\gt -\\sqrt{13} +\\sqrt{9 +2 \\sqrt{17}} -\\sqrt{9 -2 \\sqrt{17}}} \\\\\r\n& \\qquad \\underline{\\gt \\sqrt{13} -\\sqrt{9 +2 \\sqrt{17}} -\\sqrt{9 -2 \\sqrt{17}}} \\\\\r\n& \\qquad \\quad \\underline{\\gt -\\sqrt{13} -\\sqrt{9 +2 \\sqrt{17}} +\\sqrt{9 -2 \\sqrt{17}}} \\ .\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u554f\u306b\u7b54\u3048\u3088. (1)\u3000\\(a = \\sqrt{13} +\\sqrt{9 +2 \\sqrt{17}} +\\sqrt{9 -2 \\sqrt{17}}\\) \u3068\u3059\u308b\u3068\u304d, \u6574\u6570\u4fc2\u6570\u306e \\(4\\) \u6b21\u591a\u9805\u5f0f \\(f(x)\\) … \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":[129],"tags":[143,137],"class_list":["post-1274","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2015","tag-nagoya_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1274","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=1274"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1274\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}