{"id":166,"date":"2012-03-09T17:38:33","date_gmt":"2012-03-09T08:38:33","guid":{"rendered":"http:\/\/www.rainyman.net\/nest\/?p=166"},"modified":"2015-07-26T10:47:16","modified_gmt":"2015-07-26T01:47:16","slug":"%e9%ab%98%e6%ac%a1%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e8%a7%a3%e3%81%8f%e5%89%8d%e3%81%ae%e6%ba%96%e5%82%99","status":"publish","type":"post","link":"https:\/\/blog.rainyman.jp\/nest\/?p=166","title":{"rendered":"\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u524d\u306e\u6e96\u5099"},"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> \u4e8c\u9805\u5b9a\u7406<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u6839\u3068\u4fc2\u6570\u306e\u95a2\u4fc2<\/a><ul><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_2\">3.1<\/span> \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u5834\u5408<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_2\">3.2<\/span> \u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u5834\u5408<\/a><\/li><\/ul><\/li><li><a href=\"#i-6\"><span class=\"toc_number toc_depth_1\">4<\/span> \u5224\u5225\u5f0f<\/a><ul><li><a href=\"#i-7\"><span class=\"toc_number toc_depth_2\">4.1<\/span> \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u5224\u5225\u5f0f<\/a><\/li><\/ul><\/li><li><a href=\"#i-8\"><span class=\"toc_number toc_depth_1\">5<\/span> \u30c1\u30eb\u30f3\u30cf\u30a6\u30b9\u5909\u63db<\/a><\/li><li><a href=\"#i-9\"><span class=\"toc_number toc_depth_1\">6<\/span> \u8907\u7d20\u6570<\/a><\/li><li><a href=\"#1\"><span class=\"toc_number toc_depth_1\">7<\/span> 1\u306e\u7acb\u65b9\u6839<\/a><\/li><\/ul><\/div>\n<p>\u30c8\u30fc\u30e9\u30b9\u3068\u30ec\u30a4\u306e\u4ea4\u5dee\u5224\u5b9a\u306b\u306f\u56db\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u5fc5\u8981\u304c\u3042\u308b\u3068\u524d\u56de\u8a00\u53ca\u3057\u307e\u3057\u305f\uff0e<\/p>\n\n<p>\u56db\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306f\u3044\u304f\u3064\u304b\u3042\u308b\u306e\u3067\u3059\u304c\uff0c\u305d\u306e\u3044\u305a\u308c\u306e\u904e\u7a0b\u3067\u3082\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u304c\u51fa\u3066\u304d\u307e\u3059\uff0e<\/p>\n\n<p>\u306a\u306e\u3067\u307e\u305a\u306f\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u3092\u8aac\u660e\u3059\u308b\u306e\u3067\u3059\u304c\uff0c\u305d\u306e\u4e2d\u3067\u4f7f\u3046\u3044\u304f\u3064\u304b\u306e\u9053\u5177\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\uff0e\n\u4e2d\u9ad8\u30ec\u30d9\u30eb\u306e\u3082\u306e\u3070\u3063\u304b\u308a\u3067\u3059\u304c\uff0c\u3042\u304f\u307e\u3067\u3053\u3053\u306f\u30e1\u30e2\u306a\u306e\u3067\u60aa\u3057\u304b\u3089\u305a\uff0e<\/p>\n\n<h2><span id=\"i\">\u4e8c\u9805\u5b9a\u7406<\/span><\/h2>\n\n<p>$$ (a+b)^{n}=\\sum^n_{k=0}{}_n C_k a^{n-k}b^{k} $$<\/p>\n\n<p>$${}_n C_k$$\u306f\u7d44\u307f\u5408\u308f\u305b\uff0e<\/p>\n\n<div>\\({}_n C_k=\\frac{{}_n P_{k}}{k!} = \\frac{n!}{(n-k)!k!}\\)<\/div>\n\n<p><br \/><\/p>\n\n<p>\u3068\u304f\u306b$$n=2, n=3, n=4$$\u3092\u3053\u308c\u304b\u3089\u4f7f\u3046\u306e\u3067\u66f8\u304d\u4e0b\u3057\u3066\u304a\u304d\u307e\u3059\uff0e<\/p>\n\n<div>\\(\\begin{array} \\\\\n(a+b)^2 = a^2 + 2ab + b^2 \\\\\n(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \\\\\n(a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 \\\\\n\\end{array}\\)<\/div>\n\n<p><br \/><\/p>\n\n<h2><span id=\"i-2\">\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3<\/span><\/h2>\n\n<p>\u3053\u308c\u306f\u304a\u99b4\u67d3\u307f\u3067\u3059\u306d\uff0e\u4e00\u5fdc\u5c0e\u51fa\u904e\u7a0b\u3092\u5168\u90e8\u66f8\u3044\u3066\u304a\u304d\u307e\u3059\uff0e<\/p>\n\n<div>\\(\\begin{array}\nAx^2 + Bx + C = 0  \\\\\nA(x^2 + \\frac{B}{A}x) + C = 0  \\\\\nA\\left((x + \\frac{B}{2A})^2 &#8211; (\\frac{B}{2A})^2\\right) + C = 0  \\\\\nA(x + \\frac{B}{2A})^2 &#8211; A\\cdot(\\frac{B}{2A})^2 + C = 0  \\\\\nA(x + \\frac{B}{2A})^2 &#8211; A\\cdot\\frac{B^2}{4A^2} + C = 0  \\\\\nA(x + \\frac{B}{2A})^2 &#8211; \\frac{B^2}{4A} + C = 0  \\\\\nA(x + \\frac{B}{2A})^2 = \\frac{B^2}{4A} &#8211; C  \\\\\n(x + \\frac{B}{2A})^2 = \\frac{\\frac{B^2}{4A} &#8211; C}{A}  \\\\\n(x + \\frac{B}{2A})^2 = \\frac{\\frac{B^2 &#8211; 4AC}{4A}}{A}  \\\\\n(x + \\frac{B}{2A})^2 = \\frac{B^2 &#8211; 4AC}{4A^2}  \\\\\nx + \\frac{B}{2A} = \\pm \\sqrt{\\frac{B^2 &#8211; 4AC}{4A^2}}  \\\\\nx + \\frac{B}{2A} = \\frac{\\pm \\sqrt{B^2 &#8211; 4AC}}{2A}  \\\\\nx = -\\frac{B}{2A} + \\frac{\\pm \\sqrt{B^2 &#8211; 4AC}}{2A}  \\\\\nx = \\frac{-B \\pm \\sqrt{B^2 &#8211; 4AC}}{2A}  \\\\\n\\end{array}\\)<\/div>\n\n<p><br \/><\/p>\n\n<h2><span id=\"i-3\">\u6839\u3068\u4fc2\u6570\u306e\u95a2\u4fc2<\/span><\/h2>\n\n<h3><span id=\"i-4\">\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u5834\u5408<\/span><\/h3>\n\n<p>\u4e8c\u6b21\u65b9\u7a0b\u5f0f$$Ax^2 + Bx + C = 0$$\u306e\u4e8c\u3064\u306e\u6839\u304c$$\\alpha, \\beta$$\u3067\u3042\u308b\u3068\u304d\uff0c<\/p>\n\n<div>\\(\\begin{array} \\\\\n(x &#8211; \\alpha)(x &#8211; \\beta)=0 \\\\\nx^2 &#8211; (\\alpha + \\beta)x + \\alpha\\beta=0 \\\\\n\\end{array}\\)<\/div>\n\n<p><br \/><\/p>\n\n<p>\u6839\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u306f\uff0c<\/p>\n\n<div>\\(\\begin{array} \\\\\nAx^2 + Bx + C=0 \\\\\nx^2 + \\frac{B}{A}x + \\frac{C}{A}=0 \\\\\n\\end{array}\\)<\/div>\n\n<p>\u304b\u3089<\/p>\n\n<div>\\( \\begin{array} \\\\\n\\alpha + \\beta=-\\frac{B}{A} \\\\\n\\alpha\\beta=\\frac{C}{A} \\\\\n\\end{array}\\)<\/div>\n\n<p>\u3068\u306a\u308b\uff0e<\/p>\n\n<h3><span id=\"i-5\">\u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u5834\u5408<\/span><\/h3>\n\n<p>\u4e09\u6b21\u65b9\u7a0b\u5f0f$$Ax^3 + Bx^2 + Cx + D = 0$$\u306e\u4e09\u3064\u306e\u6839\u304c$$\\alpha, \\beta, \\gamma$$\u3067\u3042\u308b\u3068\u304d\uff0c<\/p>\n\n<div>\\(\\begin{array} \\\\\n(x &#8211; \\alpha)(x &#8211; \\beta)(x &#8211; \\gamma)=0 \\\\\n(x^2 -(\\alpha + \\beta)x + \\alpha\\beta)(x &#8211; \\gamma)=0 \\\\\nx^3 -(\\alpha + \\beta)x^2 + \\alpha\\beta x &#8211; \\gamma x^2 + \\gamma(\\alpha + \\beta)x &#8211; \\alpha\\beta\\gamma)=0 \\\\\nx^3 -(\\alpha + \\beta + \\gamma)x^2 + (\\alpha\\beta + \\alpha\\gamma + \\beta\\gamma)x &#8211; \\alpha\\beta\\gamma=0 \\\\\n\\end{array}\\)<\/div>\n\n<p>\u6839\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u306f\uff0c<\/p>\n\n<div>\\(\\begin{array} \\\\\nAx^3 + Bx^2 + Cx + D = 0 \\\\\nx^3 + \\frac{B}{A}x^2 + \\frac{C}{A}x + \\frac{D}{A}=0 \n\\end{array}\\)<\/div>\n\n<p>\u304b\u3089<\/p>\n\n<div>\\(\\begin{array} \\\\\n\\alpha + \\beta + \\gamma = -\\frac{B}{A} \\\\\n\\alpha\\beta + \\alpha\\gamma + \\beta\\gamma = \\frac{C}{A} \\\\\n\\alpha\\beta\\gamma = &#8211; \\frac{D}{A} \\\\\n\\end{array}\\)<\/div>\n\n<p>\u3068\u306a\u308b\uff0e<\/p>\n\n<h2><span id=\"i-6\">\u5224\u5225\u5f0f<\/span><\/h2>\n\n<p>n\u6b21\u65b9\u7a0b\u5f0f\u306b\u306f\u91cd\u6839\uff0c\u865a\u6839\u3092\u542b\u3081\u3066n\u500b\u306e\u6839\u304c\u5b58\u5728\u3059\u308b\uff0e\n\u3053\u306en\u500b\u306e<strong>\u6839\u306e\u5168\u3066\u306e\u7d44\u307f\u5408\u308f\u305b\u306e\u5dee\u306e\u7dcf\u4e57<\/strong>\u3092\u8a08\u7b97\u3059\u308b\u3068\u91cd\u6839\u306e\u6709\u7121\u304c\u5206\u304b\u308b\n(\u3069\u308c\u304b\u4e00\u3064\u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u30bc\u30ed\u306b\u306a\u308c\u3070\u5f0f\u5168\u4f53\u304c\u30bc\u30ed\u306b\u306a\u308b\u305f\u3081)\uff0e\n\u65b9\u7a0b\u5f0f\u306e\u6b21\u6570\u306b\u3088\u3063\u3066\u306f\u865a\u6839\u3092\u542b\u3080\u306e\u304b\u3068\u3044\u3063\u305f\u3053\u3068\u3082\u5206\u304b\u308b\uff0e<\/p>\n\n<p>n\u6b21\u65b9\u7a0b\u5f0f\u306e\u6839\u3092$$a_{1},a_{2},a_{3},\\ldots,a_{n}$$\u3068\u3057\u3066\u5224\u5225\u5f0f$$D$$\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\uff0e<\/p>\n\n<div>\\( D\\equiv\\prod^{}_{1\\leq i<j\\leq n}(a_i-a_j)^2 [\/latex]<\/div>\n\n<p><br \/><\/p>\n\n<p>\u4e8c\u4e57\u304c\u5165\u3063\u3066\u3044\u308b\u306e\u306f\uff0c\u6839\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3067$$D$$\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u305f\u3081\uff0e<\/p>\n\n<p>\u307e\u305f\u4e0a\u5f0f\u3067\u5224\u5225\u5f0f\u3092\u5c0e\u304f\u3068\u5206\u6bcd\u306b\u6700\u5927\u6b21\u6570\u306e\u4fc2\u6570$$A$$\u304c\u6b8b\u308b\u306e\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\u5834\u5408\u3082\u3042\u308b\uff08\u3053\u3063\u3061\u306e\u65b9\u304c\u4e00\u822c\u7684\u304b\u3082\uff09\uff0e\n$$ D\\equiv{A^{2(n-1)}}\\prod^{}_{1\\leq i<j\\leq n}(a_i-a_j)^2 $$<\/p>\n\n<h3><span id=\"i-7\">\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u5224\u5225\u5f0f<\/span><\/h3>\n\n<p>\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306f\u4e8c\u3064\u3057\u304b\u306a\u3044\u306e\u3067\u5224\u5225\u5f0f\u306f\u6bd4\u8f03\u7684\u7c21\u5358\u3067\u3059\uff0e<\/p>\n\n<p>\u4e8c\u6b21\u65b9\u7a0b\u5f0f$$Ax^2 + Bx + C = 0$$\u306e\u89e3\u304c$$\\alpha, \\beta$$\u3068\u3059\u308b\u3068<\/p>\n\n<div>[latex]\\begin{array} \\\\\nD= A^2(\\alpha &#8211; \\beta)^2 \\\\\nD= A^2(\\alpha^2 &#8211; 2\\alpha\\beta + \\beta^2) \\\\\nD= A^2(\\alpha^2 + \\beta^2 &#8211; 2\\alpha\\beta) \\\\\nD= A^2\\left((\\alpha + \\beta)^2 &#8211; 2\\alpha\\beta &#8211; 2\\alpha\\beta\\right) \\\\\nD= A^2\\left((\\alpha + \\beta)^2 &#8211; 4\\alpha\\beta\\right) \\\\\n\\end{array}\\)<\/div>\n\n<p>\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u4f7f\u3046\u3068<\/p>\n\n<div>\\(\\begin{array} \\\\\nD= A^2\\left((\\frac{-B}{A})^2 &#8211; 4\\frac{C}{A}\\right) \\\\\nD= A^2\\left(\\frac{B^2}{A^2} &#8211; \\frac{4AC}{A^2}\\right) \\\\\nD= A^2\\frac{B^2 &#8211; 4AC}{A^2} \\\\\nD= B^2 &#8211; 4AC \\\\\n\\end{array}\\)<\/div>\n\n<p>\u3068\u3044\u3046\u308f\u3051\u3067\u304a\u306a\u3058\u307f\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3057\u305f\uff0e<\/p>\n\n<h2><span id=\"i-8\">\u30c1\u30eb\u30f3\u30cf\u30a6\u30b9\u5909\u63db<\/span><\/h2>\n\n<p>n\u6b21\u65b9\u7a0b\u5f0f$$ a_{0}x^n + a_{1}x^{n-1} + a_{2}x^{x-2} + \\ldots + a_{n-1}x + a_{n}=0 $$\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c<\/p>\n\n<div>\\(\nx=u-\\frac{a_{1}}{{}_n C_{n-1}a_{0}}\n\\)<\/div>\n\n<p>\u3068\u7f6e\u304f\u3068n-1\u6b21\u306e\u9805\u3092\u6d88\u53bb\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\n\n<p>\u4f8b)\n$$ Ax^2 + Bx^2 + C = 0 $$\n$$ x=u-\\frac{B}{2A} $$\u3068\u7f6e\u304f\uff0e<\/p>\n\n<div>\\(\\begin{array} \\\\\nA\\left(u-\\frac{B}{2A}\\right)^2 + B\\left(u-\\frac{B}{2A}\\right) + C = 0 \\\\\nA\\left(u^2 &#8211; \\frac{B}{A}u + \\frac{B^2}{4A^2}\\right) + Bu &#8211; \\frac{B^2}{2A} + C = 0 \\\\\nAu^2 &#8211; Bu + \\frac{B^2}{4A} + Bu &#8211; \\frac{B^2}{2A} + C = 0 \\\\\nAu^2 \\underline{ &#8211; Bu + Bu }+ \\frac{B^2}{4A} &#8211; \\frac{B^2}{2A} + C = 0 \\\\\nAu^2 &#8211; \\frac{B^2}{4A} + C = 0 \\\\\n\\end{array}\\)<\/div>\n\n<p>\u3053\u306e\u307e\u307e$$u$$\u306b\u3064\u3044\u3066\u6574\u7406\u3057\u3066\u3044\u304f\u3068\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u516c\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\uff0e<\/p>\n\n<div>\\(\\begin{array} \\\\\nAu^2 = \\frac{B^2}{4A} &#8211; C \\\\\nAu^2 = \\frac{B^2-4AC}{4A} \\\\\nu^2 = \\frac{B^2-4AC}{4A^2} \\\\\nu = \\pm\\sqrt{\\frac{B^2-4AC}{4A^2}} \\\\\nu = \\frac{\\pm\\sqrt{B^2-4AC}}{2A} \\\\\nx + \\frac{B}{2A} = \\frac{\\pm\\sqrt{B^2-4AC}}{2A} \\\\\nx = \\frac{-B}{2A} + \\frac{\\pm\\sqrt{B^2-4AC}}{2A} \\\\\nx = \\frac{-B\\pm\\sqrt{B^2-4AC}}{2A} \\\\\n\\end{array}\\)<\/div>\n\n<h2><span id=\"i-9\">\u8907\u7d20\u6570<\/span><\/h2>\n\n<p>$$ a + bi (a,b\\in {\\bf R}) $$\u3067\u8868\u3055\u308c\u308b\u6570\u3092\u8907\u7d20\u6570\u3068\u3044\u3044\uff0ca\u3092\u5b9f\u90e8,b\u3092\u865a\u90e8\u3068\u3044\u3046\uff0e\n$$i$$\u306f\u865a\u6570\u5358\u4f4d\u3068\u3044\u3044$$ x^2 + 1 = 0 $$\u306e\u6839\u306e\u4e00\u3064\u3067\u3042\u308b\uff0e<\/p>\n\n<p>$$i$$\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6301\u3064\uff0e\n$$ i^2 = -1 $$, $$ i = \\sqrt{-1} $$<\/p>\n\n<p>$$z$$\u304c\u8907\u7d20\u6570\u3067\u3042\u308b\u3068\u304d\uff0c$$z$$\u306e\u5b9f\u90e8\u3092$$Re z$$\uff0c\u865a\u90e8\u3092$$Im z$$\u306a\u3069\u3068\u66f8\u304f\u5834\u5408\u304c\u3042\u308b\uff0e\n$$z=a + bi$$\u306b\u5bfe\u3057\u3066$$a &#8211; bi$$\u3067\u3042\u308b\u8907\u7d20\u6570\u3092\u5171\u5f79\u306a\u8907\u7d20\u6570\u3068\u3044\u3044\uff0c$$\\overline{z}$$\u3068\u66f8\u304f\uff0e<\/p>\n\n<h2><span id=\"1\">1\u306e\u7acb\u65b9\u6839<\/span><\/h2>\n\n<p>\u4e09\u6b21\u65b9\u7a0b\u5f0f$$ (x-1)(x^2 + x + 1)=0 $$\u306e\u6839\u3092\u8003\u3048\u308b\uff0e\n\u3053\u306e\u65b9\u7a0b\u5f0f\u306f$$ x^3=1 $$\u3068\u7b49\u3057\u3044\uff0e<\/p>\n\n<div>\\(\\begin{array} \\\\\n(x-1)(x^2 + x + 1)=0 \\\\\nx^3 + x^2 + x &#8211; x^2 -x -1=0 \\\\\nx^3-1=0 \\\\\nx^3=1 \\\\\n\\end{array}\\)<\/div>\n\n<p>\u6839\u306e\u4e00\u3064\u304c1\u3067\u3042\u308b\u3053\u3068\u306f\u81ea\u660e\u3067\u3042\u308b\uff0e<\/p>\n\n<p>\u3067\u306f\u3053\u306e\u5f0f\u306e\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u90e8\u5206$$ x^2 + x + 1=0 $$\u3092\u89e3\u304f\u3068\uff0c<\/p>\n\n<div>\\(\\begin{array} \\\\\nx=\\frac{-(1)\\pm\\sqrt{1^2 &#8211; 4\\cdot 1 \\cdot 1}}{2\\cdot 1} \\\\\nx=\\frac{-1\\pm\\sqrt{1 &#8211; 4}}{2} \\\\\nx=\\frac{-1\\pm\\sqrt{-3}}{2} \\\\\nx=\\frac{-1\\pm\\sqrt{3\\cdot (-1)}}{2} \\\\\nx=\\frac{-1\\pm\\sqrt{3\\cdot i^2}}{2} \\\\\nx=\\frac{-1\\pm\\sqrt{3}\\cdot\\sqrt{i^2}}{2} \\\\\nx=\\frac{-1\\pm\\sqrt{3}i}{2} \\\\\n\\end{array}\\)<\/div>\n\n<p>\u3053\u306e\u4e92\u3044\u306b\u5171\u5f79\u306a\u6839\u306e\u4e00\u65b9\u3092$$\\omega$$\u3068\u66f8\u304f\u5834\u5408\u304c\u3042\u308b\uff0e<\/p>\n\n<p>1\u306e\u7acb\u65b9\u6839\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff0e\n$$ \\sqrt[3]{1}=1, \\frac{-1+\\sqrt{3}i}{2}, \\frac{-1-\\sqrt{3}i}{2} $$<\/p>\n\n<p>\u4efb\u610f\u306e\u5b9f\u6570$$A$$\u306e\u7acb\u65b9\u6839\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff0e<\/p>\n\n<div>\\(\\begin{array} \\\\\n\\sqrt[3]{A}=\\sqrt[3]{A\\cdot 1} \\\\\n=\\sqrt[3]{A}\\cdot\\sqrt[3]{1} \\\\\n=\\sqrt[3]{A}\\cdot 1, \\sqrt[3]{A}\\cdot \\omega, \\sqrt[3]{A}\\cdot \\overline{\\omega} \\\\\n\\end{array}\\)<\/div>\n\n<p>\u307e\u305f\uff0c$$\\omega$$\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6027\u8cea\u304c\u3042\u308b\uff0e<\/p>\n\n<p>$$ \\omega^2=\\overline{\\omega}=\\omega^{-1} $$<\/p>\n\n<p>$$ \\omega^{-1}=\\frac{1}{\\omega}=\\frac{\\omega^2}{\\omega^3}=\\frac{\\omega2}{1}=\\omega^2 $$<\/p>\n\n<p>$$\\omega=\\frac{-1+\\sqrt{3}i}{2}$$\u3068\u3059\u308b\u3068\uff0c<\/p>\n\n<div>\\(\\begin{array} \\\\\n\\omega^2 = \\left(\\frac{-1+\\sqrt{3}i}{2}\\right)^2 \\\\\n=\\left(\\frac{-1}{2} + \\frac{\\sqrt{3}i}{2}\\right)^2 \\\\\n=\\left(\\frac{-1}{2}\\right)^2 + 2\\cdot\\frac{-1}{2}\\cdot\\frac{\\sqrt{3}i}{2} + \\left(\\frac{\\sqrt{3}i}{2}\\right)^2 \\\\\n=\\frac{1}{4} &#8211; \\frac{\\sqrt{3}i}{2} &#8211; \\frac{3}{4} \\\\\n=\\frac{-2}{4} &#8211; \\frac{\\sqrt{3}i}{2} \\\\\n=\\frac{-1}{2} &#8211; \\frac{\\sqrt{3}i}{2} \\\\\n=\\frac{-1 &#8211; \\sqrt{3}i}{2} \\\\\n=\\overline{\\omega} \\\\\n\\end{array}\\)<\/div>\n\n<hr \/>\n\n<p>\u3053\u306e\u304f\u3089\u3044\u304b\u306a\uff0e\u5f8c\u3067\u66f8\u304d\u8db3\u3059\u304b\u3082\uff0e<\/p>\n\n<p>\u53c2\u8003:<\/p>\n\n<ul>\n<li><a href=\"http:\/\/www004.upp.so-net.ne.jp\/s_honma\/polynomial\/discriminant.htm\">\u5224\u5225\u5f0f &#8211; \u79c1\u306e\u5099\u5fd8\u9332<\/a><\/li>\n<li><a href=\"http:\/\/www.amazon.co.jp\/dp\/448601863X\/ref=cm_sw_r_tw_dp_upCwpb0R20R1A\">\u30aa\u30a4\u30e9\u30fc\u306e\u8d08\u7269<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u6b211 \u4e8c\u9805\u5b9a\u74062 \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e33 \u6839\u3068\u4fc2\u6570\u306e\u95a2\u4fc23.1 \u4e8c\u6b21\u65b9\u7a0b\u5f0f\u306e\u5834\u54083.2 \u4e09\u6b21\u65b9\u7a0b\u5f0f\u306e\u5834\u54084 \u5224\u5225\u5f0f5 \u30c1\u30eb\u30f3\u30cf\u30a6\u30b9\u5909\u63db6 \u8907\u7d20\u65707 1\u306e\u7acb\u65b9\u6839 \u30c8\u30fc\u30e9\u30b9\u3068\u30ec\u30a4\u306e\u4ea4\u5dee\u5224\u5b9a\u306b\u306f\u56db\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u5fc5\u8981\u304c\u3042\u308b\u3068\u524d\u56de\u8a00\u53ca [&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\/166"}],"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=166"}],"version-history":[{"count":79,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions"}],"predecessor-version":[{"id":1307,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions\/1307"}],"wp:attachment":[{"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.rainyman.jp\/nest\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}