{"id":321,"date":"2012-03-13T11:27:52","date_gmt":"2012-03-13T02:27:52","guid":{"rendered":"http:\/\/www.rainyman.net\/nest\/?p=321"},"modified":"2015-07-26T10:48:03","modified_gmt":"2015-07-26T01:48:03","slug":"%e5%9b%9b%e6%ac%a1%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e8%a7%a3%e6%b3%95","status":"publish","type":"post","link":"https:\/\/blog.rainyman.jp\/nest\/?p=321","title":{"rendered":"\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5"},"content":{"rendered":"<div id=\"toc_container\" class=\"no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u30d5\u30a7\u30e9\u30fc\u30ea\u306e\u89e3\u6cd5<\/a><ul><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_2\">1.1<\/span> \u4e09\u6b21\u306e\u9805\u3092\u6d88\u53bb\u3059\u308b<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_2\">1.2<\/span> \u5909\u6570\u306e\u7f6e\u304d\u63db\u3048<\/a><\/li><\/ul><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">2<\/span> \u7279\u6b8a\u306a\u5834\u5408<\/a><ul><li><a href=\"#beta0\"><span class=\"toc_number toc_depth_2\">2.1<\/span> $$\\beta=0$$\u306e\u5834\u5408<\/a><\/li><li><a href=\"#gamma0\"><span class=\"toc_number toc_depth_2\">2.2<\/span> $$\\gamma=0$$\u306e\u5834\u5408<\/a><\/li><\/ul><\/li><\/ul><\/div>\n<p>\u672c\u984c\u3067\u3042\u308b\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u3067\u3059\uff0e\u30d5\u30a7\u30e9\u30fc\u30ea\u306e\u89e3\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\uff0e\n\u53c2\u8003\u306f\uff0c\u307e\u305f\u4f8b\u306b\u3088\u3063\u3066<a href=\"http:\/\/www.amazon.co.jp\/%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC%E3%81%AE%E8%B4%88%E7%89%A9%E2%80%95%E4%BA%BA%E9%A1%9E%E3%81%AE%E8%87%B3%E5%AE%9Dei%CF%80--1%E3%82%92%E5%AD%A6%E3%81%B6-%E5%90%89%E7%94%B0-%E6%AD%A6\/dp\/448601863X\/ref=sr_1_1?s=books&#038;ie=UTF8&#038;qid=1331536701&#038;sr=1-1\">\u30aa\u30a4\u30e9\u30fc\u306e\u8d08\u7269<\/a>\u3068<a href=\"http:\/\/en.wikipedia.org\/wiki\/Quartic_function\">Wikipedia(en)<\/a>\u3067\u3059\uff0e<\/p>\n\n<p>\u53cc\u65b9\u3084\u308a\u65b9\u304c\u82e5\u5e72\u7570\u306a\u308b\u306e\u3067\u3059\u304c\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u8d08\u7269\u3067\u66f8\u304b\u308c\u3066\u3044\u308b\u65b9\u304c\u7c21\u6f54\u306a\u306e\u3067\u305d\u3061\u3089\u306e\u65b9\u6cd5\u3067\u8aac\u660e\u3057\u307e\u3059(\u81ea\u5206\u3067\u308f\u304b\u308a\u3084\u3059\u3044\u3088\u3046\u306b\u3061\u3087\u3063\u3068\u8aac\u660e\u306f\u5909\u3048\u307e\u3059\u304c)\uff0e<\/p>\n\n<h2><span id=\"i\">\u30d5\u30a7\u30e9\u30fc\u30ea\u306e\u89e3\u6cd5<\/span><\/h2>\n\n<h3><span id=\"i-2\">\u4e09\u6b21\u306e\u9805\u3092\u6d88\u53bb\u3059\u308b<\/span><\/h3>\n\n<p>\u307e\u305a\uff0c\u30c1\u30eb\u30f3\u30cf\u30a6\u30b9\u5909\u63db\u3067\u4e09\u6b21\u306e\u9805\u3092\u524a\u9664\u3057\u3066\uff0c\u4e21\u8fba\u3092\u5b8c\u5168\u5e73\u65b9\u5f0f\u306b\u3059\u308b\u3088\u3046\u306a\u5b9a\u6570\u3092\u633f\u5165\u3057\u307e\u3059\uff0e\n\u3053\u306e\u5b9a\u6570\u3092\u5f97\u308b\u904e\u7a0b\u3067\u4e09\u6b21\u65b9\u7a0b\u5f0f\uff08\u5206\u89e3\u65b9\u7a0b\u5f0f\uff09\u3092\u89e3\u304d\u307e\u3059\uff0e\u6700\u7d42\u5b9a\u671f\u306b\uff0c\u5b8c\u5168\u5e73\u65b9\u5f0f\u306b\u3057\u305f\u4e21\u8fba\u3092\u958b\u5e73\u3057\u3066\u89e3\u3092\u5f97\u307e\u3059\uff0e<\/p>\n\n<div>\\(Ax^4 + Bx^3 + Cx^2 + Dx + E = 0\\)<\/div>\n\n<div>\\(x=u-\\frac{B}{4A}\\)<\/div>\n\n<p>\u3068\u7f6e\u304f\uff0e<\/p>\n\n<div>\\(A\\left(u-\\frac{B}{4A}\\right)^4 + B\\left(u-\\frac{B}{4A}\\right)^3 + C\\left(u-\\frac{B}{4A}\\right)^2 + D\\left(u-\\frac{B}{4A}\\right) + E = 0\\)<\/div>\n\n<div>\\(A\\left(u^4 &#8211; 4\\cdot\\frac{B}{4A}u^3 + 6\\cdot\\left(\\frac{B}{4A}\\right)^{2}u^{2} &#8211; 4\\cdot\\left(\\frac{B}{4A}\\right)^{3}u + \\left(\\frac{B}{4A}\\right)^{4}\\right)\\)<\/div>\n\n<div>\\(+B\\left(u^3 &#8211; 3\\cdot\\frac{B}{4A}u^2 + 3\\cdot\\left(\\frac{B}{4A}\\right)^{2}u &#8211; \\left(\\frac{B}{4A}\\right)^{3}\\right)\\)<\/div>\n\n<div>\\(+C\\left(u^2 &#8211; 2\\cdot\\frac{B}{4A}u + \\left(\\frac{B}{4A}\\right)^{2}\\right)\\)<\/div>\n\n<div>\\(+D\\left(u &#8211; \\frac{B}{4A}\\right) + E = 0\\)<\/div>\n\n<div>\\(A\\left(u^4 &#8211; \\frac{B}{A}u^3 + \\frac{3B^2}{8A^2}u^{2} -\\frac{B^3}{16A^3}u + \\frac{B^4}{256A^4}\\right)\\)<\/div>\n\n<div>\\(+B\\left(u^3 &#8211; \\frac{3B}{4A}u^2 + \\frac{3B^2}{16A^2}u &#8211; \\frac{B^3}{64A^3}\\right)\\)<\/div>\n\n<div>\\(+C\\left(u^2 &#8211; \\frac{B}{2A}u + \\frac{B^2}{16A^2}\\right)\\)<\/div>\n\n<div>\\(+D\\left(u &#8211; \\frac{B}{4A}\\right) + E = 0\\)<\/div>\n\n<div>\\(Au^4 &#8211; Bu^3 + \\frac{3B^2}{8A}u^{2} -\\frac{B^3}{16A^2}u + \\frac{B^4}{256A^3}\\)<\/div>\n\n<div>\\(+Bu^3 &#8211; \\frac{3B^2}{4A}u^2 + \\frac{3B^3}{16A^2}u &#8211; \\frac{B^4}{64A^3}\\)<\/div>\n\n<div>\\(+Cu^2 &#8211; \\frac{BC}{2A}u + \\frac{B^{2}C}{16A^2}\\)<\/div>\n\n<div>\\(+Du &#8211; \\frac{BD}{4A} + E = 0\\)<\/div>\n\n<div>\\(Au^4 + \\left(\\frac{3B^2}{8A} &#8211; \\frac{3B^2}{4A} + C\\right)u^2  + \\left(-\\frac{B^3}{16A^2} + \\frac{3B^3}{16A^2}  &#8211; \\frac{BC}{2A} + D\\right)u\\)<\/div>\n\n<div>\\( + \\frac{B^4}{256A^3} &#8211; \\frac{B^4}{64A^3} + \\frac{B^{2}C}{16A^2} &#8211; \\frac{BD}{4A} + E = 0\\)<\/div>\n\n<div>\\(Au^4 + \\left(\\frac{3B^2 -6B^2}{8A} + C\\right)u^2  + \\left(\\frac{3B^3 &#8211; B^3}{16A^2} &#8211; \\frac{BC}{2A} + D\\right)u\\)<\/div>\n\n<div>\\( + \\frac{B^4 &#8211; 4B^4}{256A^3} + \\frac{B^{2}C}{16A^2} &#8211; \\frac{BD}{4A} + E = 0\\)<\/div>\n\n<div>\\(u^4+\\frac{1}{A}\\left(\\frac{-3B^2}{8A}+C\\right)u^2+\\frac{1}{A}\\left(\\frac{2B^3}{16A^2}-\\frac{BC}{2A}+D\\right)u+ \\frac{-3B^4}{256A^4}+\\frac{B^{2}C}{16A^3}-\\frac{BD}{4A^2}+\\frac{E}{A}= 0\\)<\/div>\n\n<div>\\(u^4+\\left(\\frac{-3B^2}{8A^2}+\\frac{C}{A}\\right)u^2+\\left(\\frac{B^3}{8A^3}-\\frac{BC}{2A^2}+\\frac{D}{A}\\right)u+ \\frac{-3B^4}{256A^4}+\\frac{B^{2}C}{16A^3}-\\frac{BD}{4A^2}+\\frac{E}{A}= 0\\)<\/div>\n\n<p>$$u^3$$\u306e\u9805\u304c\u6d88\u3048\u307e\u3057\u305f\uff0e<\/p>\n\n<div>\\(\\alpha=\\frac{-3B^2}{8A^2}+\\frac{C}{A}\\)<\/div>\n\n<div>\\(\\beta=\\frac{B^3}{8A^3}-\\frac{BC}{2A^2}+\\frac{D}{A}\\)<\/div>\n\n<div>\\(\\gamma=\\frac{-3B^4}{256A^4}+\\frac{B^{2}C}{16A^3}-\\frac{BD}{4A^2}+\\frac{E}{A}\\)<\/div>\n\n<p>\u3068\u7f6e\u3044\u3066\uff0c<\/p>\n\n<div>\\(u^4 + \\alpha u^2 + \\beta u + \\gamma = 0\\)<\/div>\n\n<p>\u3053\u3053\u304b\u3089\u672c\u984c\u306b\u5165\u308a\u307e\u3059\uff0e<\/p>\n\n<h3><span id=\"i-3\">\u5909\u6570\u306e\u7f6e\u304d\u63db\u3048<\/span><\/h3>\n\n<div>\\(u^4 + \\alpha u^2 + \\beta u + \\gamma = 0\\)<\/div>\n\n<div>\\(u^4 = -\\alpha u^2 &#8211; \\beta u &#8211; \\gamma\\)<\/div>\n\n<p>\u4e21\u8fba\u3092$$u$$\u306b\u95a2\u3059\u308b\u5b8c\u5168\u5e73\u65b9\u5f0f\u306b\u3057\u305f\u3044\u308f\u3051\u3067\u3059\u304c\uff0c\u3053\u3053\u3067$$zu^2 + \\frac{z^2}{4}$$\u3068\u3044\u3046\u9805\u3092\u4e21\u8fba\u306b\u8db3\u3057\u307e\u3059\uff0e<\/p>\n\n<div>\\(u^4 + zu^2 + \\frac{z^2}{4}= -\\alpha u^2 &#8211; \\beta u &#8211; \\gamma + zu^2 + \\frac{z^2}{4}\\)<\/div>\n\n<p>\u30db\u30f3\u30c8\u306b\u305d\u3093\u306a\u3053\u3068\u3057\u3066\u3044\u3044\u306e\uff1f\u3068\u3044\u3046\u6c17\u3082\u3057\u307e\u3059\u304c\uff0c\u4e21\u8fba\u306b\u8db3\u3057\u3066\u3044\u308b\u306e\u3067\u5dee\u3057\u5f15\u304d\u30bc\u30ed\u3067\u3059\uff0e\u3082\u3068\u306e\u65b9\u7a0b\u5f0f\u3092\u58ca\u3057\u3066\u306f\u3044\u307e\u305b\u3093\uff0e$$z$$\u306f\u4f55\u3089\u304b\u306e\u5b9a\u6570\u3060\u3068\u8003\u3048\u3066\u304f\u3060\u3055\u3044\uff0e<\/p>\n\n<p>\u4e21\u8fba\u3092$$u$$\u306b\u95a2\u3057\u3066\u6574\u7406\u3057\u307e\u3059\uff0e<\/p>\n\n<div>\\(\\left(u^2 + \\frac{z}{2}\\right)^2= (z-\\alpha)u^2 &#8211; \\beta u + \\frac{z^2}{4} &#8211; \\gamma\\)<\/div>\n\n<p>\u5de6\u8fba\u306f\u5b8c\u5168\u5e73\u65b9\u5f0f\u306b\u306a\u3063\u3066\u3044\u307e\u3059(\u305d\u3046\u306a\u308b\u3088\u3046\u306b$$zu^2 + \\frac{z^2}{4}$$\u3068\u3044\u3046\u5f0f\u3092\u9078\u3093\u3067\u308b\u308f\u3051\u3067\u3059\u304c)\uff0e\n\u53f3\u8fba\u306f$$u$$\u306e\u4e8c\u6b21\u5f0f\u306b\u306a\u3063\u3066\u3044\u307e\u3059\uff0e\u3053\u308c\u3092$$(u+?)^2$$\u3068\u3044\u3046\u5f62\u306b\u3057\u305f\u3044\u308f\u3051\u3067\u3059\uff0e\u305d\u306e\u3088\u3046\u306b\u306a\u308b$$z$$\u306e\u5024\u3092\u3053\u308c\u304b\u3089\u63a2\u3057\u307e\u3059\uff0e<\/p>\n\n<p>\u3068\u3053\u308d\u3067\uff0c\u4e8c\u6b21\u5f0f\u304c\u5b8c\u5168\u5e73\u65b9\u5f0f\u3068\u306a\u308b\u305f\u3081\u306b\u306f<strong>\u5224\u5225\u5f0f\u304c\u30bc\u30ed\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059<\/strong>\uff0e\n\u3068\u3044\u3046\u3053\u3068\u306f\uff0c\u53f3\u8fba\u306e$$u$$\u306b\u95a2\u3059\u308b\u4e8c\u6b21\u5f0f\u304b\u3089\u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u51fa\u6765\u307e\u3059\uff0e<\/p>\n\n<div>\\((-\\beta)^2 &#8211; 4(z-\\alpha)(\\frac{z^2}{4} &#8211; \\gamma)=0\\)<\/div>\n\n<p>\u6240\u8b02$$B^2 &#8211; 4AC$$\u306e\u5f62\u3067\u3059\uff0e\u3053\u306e\u5f0f\u3092$$z$$\u306b\u3064\u3044\u3066\u6574\u7406\u3059\u308b\u3068\uff0c<\/p>\n\n<div>\\(\\beta^2 &#8211; 4\\left(\\frac{1}{4}z^2(z-\\alpha) &#8211; \\gamma(z-\\alpha)\\right)=0\\)<\/div>\n\n<div>\\(\\beta^2 &#8211; z^2(z-\\alpha) + 4\\gamma(z-\\alpha)=0\\)<\/div>\n\n<div>\\(\\beta^2 &#8211; z^3 + \\alpha z^2 + 4\\gamma z &#8211; 4\\gamma\\alpha=0\\)<\/div>\n\n<div>\\(-z^3 + \\alpha z^2 + 4\\gamma z &#8211; 4\\gamma\\alpha + \\beta^2=0\\)<\/div>\n\n<div>\\(z^3 &#8211; \\alpha z^2 &#8211; 4\\gamma z + 4\\gamma\\alpha + \\beta^2=0\\)<\/div>\n\n<div>\\(z^3 &#8211; \\alpha z^2 &#8211; 4\\gamma z + \\left(4\\gamma\\alpha + \\beta^2\\right)=0\\)<\/div>\n\n<p>\u3053\u308c\u3092\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u4e09\u6b21\u5206\u89e3\u65b9\u7a0b\u5f0f\u3068\u8a00\u3044\u307e\u3059\uff0e\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306f\u524d\u56de\u3084\u3063\u305f\u306e\u3067\u7701\u7565\u3057\u307e\u3059\uff0e<\/p>\n\n<p>\u5206\u89e3\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u4e00\u3064(\u3069\u308c\u3067\u3082\u826f\u3044)\u3092$$\\Omega$$\u3068\u3059\u308b\u3068\uff0c<\/p>\n\n<div>\\(\\left(u^2 + \\frac{z}{2}\\right)^2= (z-\\alpha)u^2 &#8211; \\beta u + \\frac{z^2}{4} &#8211; \\gamma\\)<\/div>\n\n<p>\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n<div>\\(\\left(u^2 + \\frac{\\Omega}{2}\\right)^2=(\\Omega-\\alpha)u^2 &#8211; \\beta u + \\frac{\\Omega^2}{4} &#8211; \\gamma\\)<\/div>\n\n<div>\\(=(\\Omega-\\alpha)\\left(u^2 &#8211; \\frac{\\beta}{(\\Omega-\\alpha)}u + \\frac{\\frac{\\Omega^2}{4} &#8211; \\gamma}{(\\Omega-\\alpha)}\\right)\\)<\/div>\n\n<div>\\(=(\\Omega-\\alpha)\\left(\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2-\\left(\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2+\\frac{\\frac{\\Omega^2}{4}-\\gamma}{(\\Omega-\\alpha)}\\right)\\)<\/div>\n\n<div>\\(=(\\Omega-\\alpha)\\left(\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2-\\frac{\\beta^2}{4(\\Omega-\\alpha)^2}+\\frac{\\frac{\\Omega^2}{4}-\\gamma}{(\\Omega-\\alpha)}\\right)\\)<\/div>\n\n<div>\\(=(\\Omega-\\alpha)\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2-\\frac{\\beta^{2}}{4(\\Omega-\\alpha)}+\\frac{\\Omega^2}{4}-\\gamma\\)<\/div>\n\n<div>\\(=(\\Omega-\\alpha)\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2-\\frac{1}{4(\\Omega-\\alpha)}\\left(\\beta^{2}-4(\\Omega-\\alpha)\\left(\\frac{\\Omega^2}{4}-\\gamma\\right)\\right)\\)<\/div>\n\n<div>\\(=(\\Omega-\\alpha)\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2-\\frac{1}{4(\\Omega-\\alpha)}\\cdot 0\\)<\/div>\n\n<div>\\(=(\\Omega-\\alpha)\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2\\)<\/div>\n\n<div>\\(\\left(u^2 + \\frac{\\Omega}{2}\\right)^2=(\\Omega-\\alpha)\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)^2\\)<\/div>\n\n<p>\u958b\u5e73\u3057\u3066\uff0c<\/p>\n\n<div>\\(u^2 + \\frac{\\Omega}{2}=\\pm\\sqrt{\\Omega-\\alpha}\\left(u-\\frac{\\beta}{2(\\Omega-\\alpha)}\\right)\\)<\/div>\n\n<div>\\(u^2 + \\frac{\\Omega}{2}=\\pm\\sqrt{\\Omega-\\alpha}\\cdot u \\mp\\sqrt{\\Omega-\\alpha}\\cdot\\frac{\\beta}{2(\\Omega-\\alpha)}\\)<\/div>\n\n<div>\\(u^2 \\mp\\sqrt{\\Omega-\\alpha}\\cdot u + \\frac{\\Omega}{2} \\pm\\sqrt{\\Omega-\\alpha}\\cdot\\frac{\\beta}{2(\\Omega-\\alpha)}= 0\\)<\/div>\n\n<div>\\(u^2 \\mp\\sqrt{\\Omega-\\alpha}\\cdot u + \\frac{\\Omega}{2} \\pm\\frac{\\beta}{2\\sqrt{\\Omega-\\alpha}}= 0\\)<\/div>\n\n<p>\u89e3\u306e\u4e00\u822c\u5f62\u306f\uff0c<\/p>\n\n<div>\\(u=\\frac{1}{2}\\left(\\pm_{s}\\sqrt{\\Omega-\\alpha}\\pm_{t}\\sqrt{(\\Omega-\\alpha)\\mp_{s}\\left(\\frac{\\Omega}{2}+\\frac{\\beta}{2\\sqrt{\\Omega-\\alpha}}\\right)}\\right)\\)<\/div>\n\n<p>\u203b $$\\pm$$\u306e\u6dfb\u3048\u5b57\u304c\u9055\u3046\u3082\u306e\u306f\u72ec\u7acb\u306b\u5909\u5316\u3059\u308b\u3068\u8003\u3048\u3066\u304f\u3060\u3055\u3044\uff0e<\/p>\n\n<h2><span id=\"i-4\">\u7279\u6b8a\u306a\u5834\u5408<\/span><\/h2>\n\n<p>\u56db\u6b21\u65b9\u7a0b\u5f0f\u3067\u3082\uff0c\u30c1\u30eb\u30f3\u30cf\u30a6\u30b9\u5909\u63db\u5f8c\u306e<\/p>\n\n<div>\\(u^4 + \\alpha u^2 + \\beta u + \\gamma = 0\\)<\/div>\n\n<p>\u306e\u4fc2\u6570\u306b\u3088\u3063\u3066\u306f\u5f8c\u306e\u8a08\u7b97\u3092\u7701\u7565\u3067\u304d\u307e\u3059\uff0e<\/p>\n\n<h3><span id=\"beta0\">$$\\beta=0$$\u306e\u5834\u5408<\/span><\/h3>\n\n<div>\\(u^4 + \\alpha u^2 + 0\\cdot u + \\gamma = 0\\)<\/div>\n\n<div>\\(u^4 + \\alpha u^2 + \\gamma = 0\\)<\/div>\n\n<p>\u3053\u308c\u306f\u8907\u4e8c\u6b21\u65b9\u7a0b\u5f0f(biquadratic equation)\u3068\u547c\u3070\u308c\u308b\u5f62\u5f0f\u3067\u3059\uff0e\u898b\u3066\u306e\u901a\u308a$$u^2$$\u306e\u4e8c\u6b21\u5f0f\u3068\u306a\u3063\u3066\u3044\u307e\u3059\uff0e<\/p>\n\n<div>\\(u^2=\\frac{-\\alpha \\pm \\sqrt{\\alpha^2 &#8211; 4\\cdot 1 \\dot \\gamma}}{2\\cdot 1}\\)<\/div>\n\n<div>\\(u^2=\\frac{-\\alpha \\pm \\sqrt{\\alpha^2 &#8211; 4\\gamma}}{2}\\)<\/div>\n\n<div>\\(u=\\pm_{t}\\sqrt{\\frac{-\\alpha \\pm_{s} \\sqrt{\\alpha^2 &#8211; 4\\gamma}}{2}}\\)<\/div>\n\n<h3><span id=\"gamma0\">$$\\gamma=0$$\u306e\u5834\u5408<\/span><\/h3>\n\n<div>\\(u^4 + \\alpha u^2 + \\beta u + 0 = 0\\)<\/div>\n\n<div>\\(u^4 + \\alpha u^2 + \\beta u = 0\\)<\/div>\n\n<div>\\(u(u^3 + \\alpha u + \\beta)= 0\\)<\/div>\n\n<p>\u89e3\u306f$$u=0$$\u3068$$u^3 + \\alpha u + \\beta=0$$\u306e\u4e09\u3064\u306e\u6839\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n<hr \/>\n\n<p>\u3053\u308c\u3089\u3092\u4f7f\u3048\u3070\u30c8\u30fc\u30e9\u30b9\u3068\u30ec\u30a4\u306e\u4ea4\u5dee\u5224\u5b9a\u304c\u53ef\u80fd\u3067\u3059\uff0e\n\u3061\u3083\u3093\u3068\u8abf\u3079\u3066\u3044\u307e\u305b\u3093\u304c\uff0c\u30af\u30e9\u30a4\u30f3\u306e\u58fa\u306a\u3093\u304b\u3082\u56db\u6b21\u66f2\u9762\u3089\u3057\u3044\u306e\u3067\u3053\u3046\u3044\u3063\u305f\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u304c\u4f7f\u3048\u307e\u3059\uff0e<\/p>\n\n<p>\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u3057\u3066\u3053\u306e\u89e3\u6cd5\u3092\u5b9f\u88c5\u3059\u308b\u5834\u5408\u306f\u8907\u7d20\u6570\u304c\u6271\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff0eC++\u306a\u3089std::complex&lt;T&gt;\u3068\u3044\u3046\u3084\u3064\u304c\u3042\u308a\u307e\u3059\uff0e\u5b9f\u88c5\u4f8b\u306f\u3044\u305a\u308c\u8f09\u305b\u3088\u3046\u304b\u3068\u601d\u3044\u307e\u3059\uff0e<\/p>\n\n<p>\u6b21\u56de\u306f\u6570\u5024\u89e3\u6790\u306b\u3088\u308b\u6c42\u89e3\u306b\u3064\u3044\u3066\u66f8\u3053\u3046\u3068\u601d\u3044\u307e\u3059\uff0e<\/p>\n\n<p>(\u305d\u3046\u3044\u3048\u3070\u30c8\u30fc\u30e9\u30b9\u306e\u4ea4\u70b9\u306b\u304a\u3051\u308b\u6cd5\u7dda\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u66f8\u3044\u3066\u3044\u307e\u305b\u3093\u3067\u3057\u305f\uff0e\u30c8\u30fc\u30e9\u30b9\u306e\u56de\u306b\u30ea\u30f3\u30af\u3057\u305fPDF\u306b\u66f8\u3044\u3066\u3042\u308a\u307e\u3059\u30b1\u30c9\uff0e)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u6b211 \u30d5\u30a7\u30e9\u30fc\u30ea\u306e\u89e3\u6cd51.1 \u4e09\u6b21\u306e\u9805\u3092\u6d88\u53bb\u3059\u308b1.2 \u5909\u6570\u306e\u7f6e\u304d\u63db\u30482 \u7279\u6b8a\u306a\u5834\u54082.1 $$\\beta=0$$\u306e\u5834\u54082.2 $$\\gamma=0$$\u306e\u5834\u5408 \u672c\u984c\u3067\u3042\u308b\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u3067\u3059\uff0e\u30d5\u30a7\u30e9\u30fc\u30ea\u306e\u89e3\u6cd5\u306b\u3064\u3044\u3066\u8aac [&hellip;]<\/p>","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/321"}],"collection":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=321"}],"version-history":[{"count":82,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/321\/revisions"}],"predecessor-version":[{"id":1309,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/321\/revisions\/1309"}],"wp:attachment":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}