{"id":489,"date":"2012-11-25T09:51:36","date_gmt":"2012-11-25T00:51:36","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=489"},"modified":"2021-09-23T22:29:25","modified_gmt":"2021-09-23T13:29:25","slug":"thr201105","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201105\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2011\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(a\\) \u3092\u5b9f\u6570, \\(z\\) \u3092 \\(0\\) \u3067\u306a\u3044\u8907\u7d20\u6570\u3068\u3059\u308b.\r\n\\(z\\) \u306b\u5171\u5f79\u306a\u8907\u7d20\u6570\u3092 \\(\\overline{z}\\) \u3067\u8868\u3059.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u6b21\u3092\u6e80\u305f\u3059 \\(z\\) \u3092\u6c42\u3081\u3088.\r\n\\[\r\nz -1 -\\dfrac{a}{z} = 0\r\n\\]<\/li>\r\n

  2. (2)<\/strong>\u3000\u6b21\u3092\u6e80\u305f\u3059 \\(z\\) \u304c\u5b58\u5728\u3059\u308b\u3088\u3046\u306a \\(a\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.\r\n\\[\r\n\\overline{z} +1 -\\dfrac{a}{z} = 0\r\n\\]<\/li>\r\n

  3. (3)<\/strong>\u3000\u6b21\u3092\u6e80\u305f\u3059 \\(z\\) \u304c\u5b58\u5728\u3059\u308b\u3088\u3046\u306a \\(a\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.\r\n\\[\r\nz \\left( \\overline{z} \\right)^2 +\\overline{z} -\\dfrac{a}{z} = 0\r\n\\]<\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    \\[\r\nz -1 -\\dfrac{a}{z} = 0 \\ .\r\n\\]\r\n\\(z \\neq 0 \\quad ... [1]\\) \u306a\u306e\u3067, \u4e21\u8fba\u306b \\(z\\) \u3092\u639b\u3051\u3066\r\n\\[\\begin{align}\r\nz^2 -z -a & = 0 \\\\\r\n\\text{\u2234} \\quad z & = \\dfrac{1 \\pm \\sqrt{4a+1}}{2} \\ .\r\n\\end{align}\\]\r\n\u305f\u3060\u3057, \\(z=0\\) \u3068\u306a\u308b\u3068\u304d\r\n\\[\\begin{align}\r\n0^2 -0 -a & = 0 \\\\\r\n\\text{\u2234} \\quad a & = 0 \\ .\r\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d\u306b\u3064\u3044\u3066\u306f\r\n\\[\\begin{align}\r\nz^2 -z & = 0 \\\\\r\nz(z-1) & = 0 \\\\\r\n\\text{\u2234} \\quad z & = 1 \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\nz = \\underline{\\left\\{ \\begin{array}{ll} 1 & ( \\ a=0 \\text{\u306e\u3068\u304d} ) \\\\ \\dfrac{1 \\pm \\sqrt{4a+1}}{2} & ( \\ a \\neq 0 \\text{\u306e\u3068\u304d} ) \\end{array} \\right.} \\ .\r\n\\]\r\n

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

    \\[\\begin{align}\r\n\\overline{z} +1 -\\dfrac{a}{z} & = 0 \\\\\r\n\\text{\u2234} \\quad |z|^2 +z -a & = 0 \\ .\r\n\\end{align}\\]\r\n\\(z = x+yi\\) \uff08 \\(x, y\\) \u306f\u5b9f\u6570, \\(x^2+y^2 \\neq 0\\) ... [2] \uff09\u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nx^2+y^2+ x+yi -a & = 0 \\\\\r\n\\text{\u2234} \\quad x^2+y^2+ x-a +yi & = 0 \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\nx^2+y^2+ x-a =0 & , \\ y = 0 \\\\\r\nx^2+x-a & = 0 \\\\\r\n\\text{\u2234} \\quad \\left( x+\\dfrac{1}{2} \\right)^2 -\\dfrac{1}{4} & = a \\quad ... [3] \\ .\r\n\\end{align}\\]\r\n[2] \u3068\u3042\u308f\u305b\u308b\u3068, \\(x \\neq 0\\) .
    \r\n\u3057\u305f\u304c\u3063\u3066, [3] \u304c \\(x \\neq 0\\) \u3067\u3042\u308b\u89e3\u3092\u3082\u3064\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.<\/p>\r\n\"\"\r\n

    \u3088\u3063\u3066\r\n\\[\r\n\\underline{a \\geqq -\\dfrac{1}{4}} \\ .\r\n\\]\r\n

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

    \\[\\begin{align}\r\nz \\left( \\overline{z} \\right)^2 +\\overline{z} -\\dfrac{a}{z} & = 0 \\\\\r\n\\text{\u2234} \\quad |z|^4+|z|^2-a & = 0 \\ .\r\n\\end{align}\\]\r\n\\(t = |z|^2 \\ ( t \\gt 0 )\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nt^2+t-a & = 0 \\\\\r\n\\text{\u2234} \\quad \\left( t+\\dfrac{1}{2} \\right)^2 -\\dfrac{1}{4} & = a \\quad ... [4] \\ .\r\n\\end{align}\\]\r\n[4] \u304c \\(t \\gt 0\\) \u306b\u89e3\u3092\u3082\u3064\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u306e\u3067<\/p>\r\n\"\"\r\n

    \\[\r\n\\underline{a \\gt 0} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092\u5b9f\u6570, \\(z\\) \u3092 \\(0\\) \u3067\u306a\u3044\u8907\u7d20\u6570\u3068\u3059\u308b. \\(z\\) \u306b\u5171\u5f79\u306a\u8907\u7d20\u6570\u3092 \\(\\overline{z}\\) \u3067\u8868\u3059. (1)\u3000\u6b21\u3092\u6e80\u305f\u3059 \\(z\\) \u3092\u6c42\u3081\u3088. \\[ z -1 -\\dfrac … \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":[73],"tags":[148,13],"class_list":["post-489","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2011","tag-tohoku_r","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/489","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=489"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/489\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=489"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=489"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}