{"id":1379,"date":"2017-02-17T21:59:29","date_gmt":"2017-02-17T12:59:29","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1379"},"modified":"2021-09-24T21:08:45","modified_gmt":"2021-09-24T12:08:45","slug":"tkr201604","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr201604\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2016\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(z\\) \u3092\u8907\u7d20\u6570\u3068\u3059\u308b. \r\n\u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306e \\(3\\) \u70b9 \\(\\text{A} ( 1 )\\) , \\(\\text{B} ( z )\\) , \\( \\text{C} ( z^2 )\\) \u304c\r\n\u92ed\u89d2\u4e09\u89d2\u5f62\u3092\u306a\u3059\u3088\u3046\u306a \\(z\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081, \u56f3\u793a\u305b\u3088.<\/p>\r\n

\r\n\r\n

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

\u70b9 A , B , C \u306f\u3059\u3079\u3066\u7570\u306a\u308b\u306e\u3067\r\n\\[\\begin{align}\r\nz \\neq 1 , \\quad z^2 & \\neq 1 , \\quad z \\neq z^2 \\\\\r\n\\text{\u2234} \\quad z & \\neq 0 , \\pm 1 \\quad ... [1]\r\n\\end{align}\\]\r\n\\(\\triangle \\text{ABC}\\) \u304c\u92ed\u89d2\u4e09\u89d2\u5f62\u3068\u306a\u308b\u6761\u4ef6\u306f\r\n\\[\r\n\\left\\{ \\begin{array}{l} \\text{AB}^2 + \\text{BC}^2 \\gt \\text{CA}^2 \\\\ \\text{BC}^2 + \\text{CA}^2 \\gt \\text{AB}^2 \\\\ \\text{CA}^2 + \\text{AB}^2 \\gt \\text{BC}^2 \\end{array} \\right. \\quad ... [2]\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\n\\text{AB}^2 & = | z-1 |^2 \\\\\r\n\\text{BC}^2 & = | z^2-z |^2 = |z|^2 | z-1 |^2 \\\\\r\n\\text{CA}^2 & = | z^2-1 |^2 = | z+1 |^2 | z-1 |^2\r\n\\end{align}\\]\r\n[2] \u306b\u4ee3\u5165\u3057\u3066, \\(| z-1 |^2 \\gt 0\\) \u306b\u6ce8\u610f\u3059\u308c\u3070\r\n\\[\r\n\\left\\{ \\begin{array}{ll} 1+|z|^2 \\gt | z+1 |^2 & \\quad ... [3] \\\\ |z|^2 +| z+1 |^2 \\gt 1 & \\quad ... [4] \\\\ | z+1 |^2 +1 \\gt |z|^2 & \\quad ... [5] \\end{array} \\right.\r\n\\]\r\n\\(z = x +yi\\) \u3068\u304a\u3051\u3070, [3] \u3088\u308a\r\n\\[\\begin{align}\r\n1 +x^2 +y^2 & \\gt (x+1)^2 +y^2 \\\\\r\n\\text{\u2234} \\quad x & \\lt 0\r\n\\end{align}\\]\r\n[4] \u3088\u308a\r\n\\[\\begin{align}\r\n(x+1)^2 +y^2 +1 & \\gt x^2 +y^2 \\\\\r\n2x +2 & \\gt 0 \\\\\r\n\\text{\u2234} \\quad x & \\gt -1\r\n\\end{align}\\]\r\n[5] \u3088\u308a\r\n\\[\\begin{align}\r\nx^2 +y^2 +(x+1)^2 +y^2 & \\gt 1 \\\\\r\n2x^2 +2x +2y^2 & \\gt 0 \\\\\r\n\\text{\u2234} \\quad \\left( x +\\dfrac{1}{2} \\right)^2 +y^2 & \\gt \\dfrac{1}{4}\r\n\\end{align}\\]\r\n\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b \\(z\\) \u306e\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{-1 \\lt \\text{Re} \\, z \\lt 0 \\ \\text{\u304b\u3064} \\ \\left| z +\\dfrac{1}{2} \\right| \\gt \\dfrac{1}{2}}\r\n\\]\r\n\u3067\u3042\u308a, \u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306b\u56f3\u793a\u3059\u308b\u3068, \u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u3007, \u70b9\u7dda\u5883\u754c\u306f\u9664\u304f\uff09. <\/p>\r\n\"\"\r\n","protected":false},"excerpt":{"rendered":"\\(z\\) \u3092\u8907\u7d20\u6570\u3068\u3059\u308b. \u8907\u7d20\u6570\u5e73\u9762\u4e0a\u306e \\(3\\) \u70b9 \\(\\text{A} ( 1 )\\) , \\(\\text{B} ( z )\\) , \\( \\text{C} ( z^2 )\\) \u304c \u92ed\u89d2\u4e09\u89d2\u5f62\u3092\u306a\u3059\u3088\u3046\u306a \\ … \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":[150],"tags":[139,162],"class_list":["post-1379","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2016","tag-tokyo_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1379","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=1379"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1379\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}