{"id":126,"date":"2025-07-03T11:32:29","date_gmt":"2025-07-03T02:32:29","guid":{"rendered":"https:\/\/math-friend.com\/?p=126"},"modified":"2025-08-01T09:19:24","modified_gmt":"2025-08-01T00:19:24","slug":"%e3%80%90%e4%b9%9d%e5%b7%9e%e5%a4%a7%e5%ad%a6%e3%80%912%e6%ac%a1%e9%96%a2%e6%95%b0%e3%81%a83%e6%ac%a1%e9%96%a2%e6%95%b0%e3%81%ae%e5%85%b1%e9%80%9a%e6%8e%a5%e7%b7%9a","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=126","title":{"rendered":"\u3010\u4e5d\u5dde\u5927\u5b66\u5165\u8a66\u30112\u6b21\u95a2\u6570\u30683\u6b21\u95a2\u6570\u306e\u5171\u901a\u63a5\u7dda(2025)"},"content":{"rendered":"\n<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n<p class=\"has-border -border02\">2\u6b21\u95a2\u6570\\(y=x^2\\)\u306e\u30b0\u30e9\u30d5\u3068, 3\u6b21\u95a2\u6570\\(y=x^3+x^2-x-1\\)\u306e\u30b0\u30e9\u30d5\u306e\u5171\u901a\u63a5\u7dda\u3092\u6c42\u3081\u3088. (2025 \u4e5d\u5dde\u5927\u5b66)<\/p>\n\n\n\n<p>2\u6b21\u95a2\u6570\u30683\u6b21\u95a2\u6570\u306e\u5171\u901a\u63a5\u7dda\u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u3059. \u8a08\u7b97\u304c\u5c11\u3057\u3060\u3051\u30cf\u30fc\u30c9\u3067\u9ad8\u6b21\u65b9\u7a0b\u5f0f\u3082\u767b\u5834\u3059\u308b\u306e\u3067, \u8a08\u7b97\u9593\u9055\u3044\u304c\u306a\u3044\u304b\u306a\u3069\u4e0d\u5b89\u306b\u99c6\u3089\u308c\u3066\u3057\u307e\u3046\u554f\u984c\u3067\u3059. \u3053\u3053\u3067\u306f2\u3064\u306e\u89e3\u6cd5\u3092\u7d39\u4ecb\u3057\u3088\u3046\u3068\u601d\u3044\u307e\u3059.<br><br>1\u3064\u76ee\u306e\u89e3\u6cd5\u306f\u5404\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3067\\(x\\)\u5ea7\u6a19\u304c\\(a\\), \\(b\\)\u3067\u3042\u308b\u70b9\u306b\u304a\u3051\u308b\u63a5\u7dda\u3092\u305d\u308c\u305e\u308c\u6c42\u3081\u3066, \u305d\u308c\u3089\u304c\u4e00\u81f4\u3059\u308b, \u3064\u307e\u308a\u50be\u304d\u3068\u5207\u7247\u304c\u4e00\u81f4\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u306e\u3082\u3068, \\(a\\), \\(b\\)\u306e\u95a2\u4fc2\u5f0f\u3092\u5c0e\u51fa\u3057, \u6c42\u3081\u308b\u3068\u3044\u3046\u3082\u306e\u3067\u3059.<br><br>2\u3064\u76ee\u306e\u89e3\u6cd5\u306f3\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3067\\(x\\)\u5ea7\u6a19\u304c\\(b\\)\u3067\u3042\u308b\u70b9\u306b\u304a\u3051\u308b\u63a5\u7dda\u3092\u6c42\u3081\u3066, \u305d\u306e\u76f4\u7dda\u304c2\u6b21\u9593\u6570\u306e\u30b0\u30e9\u30d5\u306b\u63a5\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u304b\u3089\u6c42\u3081\u308b\u3082\u306e\u3067\u3059. \u300c2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3068\u76f4\u7dda(1\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5)\u304c\u63a5\u3059\u308b\u300d\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f, \u300c\u305d\u308c\u3089\u3092\u9023\u7acb\u3057\u3066\\(y\\)\u3092\u6d88\u53bb\u3057\u3066\u3067\u304d\u308b\\(x\\)\u306e2\u6b21\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u6301\u3064\u300d\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059. \u3053\u308c\u306f\u6559\u79d1\u66f8\u306b\u3082\u8f09\u3063\u3066\u3044\u308b\u6709\u540d\u4e8b\u5b9f\u306a\u306e\u3067\u3057\u3063\u304b\u308a\u4f7f\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046.<br><br>\u306a\u304a, \u554f\u984c\u3092\u89e3\u304f\u524d\u306b\u30b0\u30e9\u30d5\u3092\u66f8\u3044\u3066\u304a\u304f\u3068\u3053\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059. <br><br>\u3053\u3046\u3044\u3063\u305f\u554f\u984c\u3067\u306f\u6982\u5f62\u3067\u3082\u66f8\u3044\u3066\u304a\u304f\u307b\u3046\u304c, \u6c42\u3081\u305f\u63a5\u7dda\u306e\u59a5\u5f53\u6027\u3092\u78ba\u8a8d\u3067\u304d\u308b\u306e\u3067\u826f\u3044\u304b\u3068\u601d\u3044\u307e\u3059.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"708\" height=\"728\" src=\"https:\/\/math-friend.com\/wp-content\/uploads\/2025\/07\/9d8a0640b28bc68a239517cdedae40b5.png\" alt=\"\" class=\"wp-image-129\" style=\"width:506px;height:auto\" srcset=\"https:\/\/math-friend.com\/wp-content\/uploads\/2025\/07\/9d8a0640b28bc68a239517cdedae40b5.png 708w, https:\/\/math-friend.com\/wp-content\/uploads\/2025\/07\/9d8a0640b28bc68a239517cdedae40b5-292x300.png 292w\" sizes=\"(max-width: 708px) 100vw, 708px\" \/><\/figure>\n\n\n\n<p>\u3067\u306f\u307e\u305a\u306f1\u3064\u76ee\u306e\u89e3\u6cd5\u3067\u3059.<\/p>\n\n\n\n<div class=\"wp-block-group is-style-crease\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\\(y=x^2\\), \\(y=x^3+x^2-x-1\\)\u3092\u305d\u308c\u305e\u308c\u5fae\u5206\u3059\u308b\u3068, \\(y^\\prime=2x\\), \\(y^\\prime=3x^2+2x-x-1\\)\u3068\u306a\u308b\u306e\u3067, \u5404\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u4e0a\u306e\u70b9\\((a,a^2)\\), \\((b,b^3+b^2-b-1)\\)\u306b\u304a\u3051\u308b\u63a5\u7dda\u306f\u305d\u308c\u305e\u308c, <br>$$<br>\\begin{align}<br>y&amp;=2a(x-a)+a^2=2ax-a^2,\\\\[1.5ex]<br>y&amp;=(3b^2+2b-1)(x-b)+b^3+b^2-b-1\\\\[1.5ex]<br>&amp;=(3b^2+2b-1)x-2b^3-b^2-1<br>\\end{align}<br>$$\u3068\u306a\u308b.<br><br>\u3053\u306e2\u3064\u306e\u63a5\u7dda\u304c\u4e00\u81f4\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u304b\u3089, \u50be\u304d\u3068\u5207\u7247\u3092\u6bd4\u8f03\u3057\u3066.<br>$$<br>\\left\\{ \\begin{aligned}2a&amp;=3b^2+2b-1\\,\\,\\,\\,\\text{ \u30fb\u30fb\u30fb\u2460} \\\\[1.5ex] -a^2&amp;=-2b^3-b^2-1\\,\\,\\,\\,\\text{ \u30fb\u30fb\u30fb\u2461} \\end{aligned} \\right.<br>$$<br>\u3092\u5f97\u308b. \u2461\u30924\u500d\u3059\u308b\u3068, <br>$$<br>-4a^2=-8b^3-4b^2-4<br>$$<br>\u3068\u306a\u308a, \u5de6\u8fba\\(-4a^2=-(2a)^2\\)\u3088\u308a, \u2460\u3092\u4ee3\u5165\u3059\u308b\u3068,<br>$$<br>-(3b^2+2b-1)^2=-8b^3-4b^2-4<br>$$<br>\u3068\u308b. \u5c55\u958b\u3057\u3066\u6574\u7406\u3059\u308b\u3053\u3068\u3067\u4ee5\u4e0b\u306e\\(b\\)\u306b\u95a2\u3059\u308b4\u6b21\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b.<br>$$<br>9b^4+4b^3-6b^2-4b-3=0<br>$$<br>\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\\(b=1\\)\u3068\u3059\u308b\u3068\u6210\u308a\u7acb\u3064\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067, \u5de6\u8fba\u306e\\(b\\)\u306e\u6574\u5f0f\u306f\\((b-1)\\)\u3067\u5272\u308a\u5207\u308c\u308b. \u5272\u308a\u7b97\u3092\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067, <br>$$<br>(b-1)(9b^3+13b^2+7b+3)=0<br>$$<br>\u3092\u5f97\u308b. \u3053\u3053\u3067\\(b\\)\u306e3\u6b21\u5f0f\\(9b^3+13b^2+7b+3\\)\u306f\\(b=-1\\)\u3068\u3059\u308b\u3068\\(0\\)\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067, \u3053\u308c\u306f\u3055\u3089\u306b\\(b+1\\)\u3067\u5272\u308c\u308b. \u518d\u3073\u5272\u308a\u7b97\u3092\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u6700\u7d42\u7684\u306b, <br>$$<br>(b-1)(b+1)(9b^2+4b+3)=0<br>$$<br>\u3068\u306a\u308b. \\(b\\)\u306b\u95a2\u3059\u308b2\u6b21\u65b9\u7a0b\u5f0f\\(9b^2+4b+3=0\\)\u306f\u5224\u5225\u5f0f\u304c\\(4^2-4\\times 9 \\times 3 &lt;0\\)\u3068\u306a\u308a\u5b9f\u6570\u89e3\u3092\u6301\u305f\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067, \u3053\u306e\\(b\\)\u306e4\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306f\\(b=-1, 1\\)\u306e2\u3064\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b.<br><br>\u2460\u304b\u3089, \\(b=-1\\)\u306e\u3068\u304d\\(a=0\\), \\(b=1\\)\u306e\u3068\u304d\\(a=2\\)\u3068\u306a\u308a \u6c42\u3081\u308b\u5171\u901a\u63a5\u7dda\u306f, <br>$$<br>y=0\\,\\,\\mbox{\u3068}\\,\\,y=4x-4<br>$$<br>\u306e2\u3064\u3067\u3042\u308b.<\/p>\n<\/div><\/div>\n\n\n\n<p>\u6b21\u306b2\u3064\u76ee\u306e\u89e3\u6cd5\u3067\u3059.<\/p>\n\n\n\n<div class=\"wp-block-group is-style-crease\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\\(y=x^3+x^2-x-1\\)\u3092\u5fae\u5206\u3059\u308b\u3068, \\(y^\\prime=3x^2+2x-x-1\\)\u3068\u306a\u308a, \u30b0\u30e9\u30d5\u4e0a\u306e\u70b9\\((b,b^3+b^2-b-1)\\)\u306b\u304a\u3051\u308b\u63a5\u7dda\u306f,<br>$$<br>\\begin{align}<br>y&amp;=(3b^2+2b-1)(x-b)+b^3+b^2-b-1\\\\[1.5ex]<br>&amp;=(3b^2+2b-1)x-2b^3-b^2-1<br>\\end{align}<br>$$\u3068\u306a\u308b.<br><br>\u3053\u306e3\u6b21\u95a2\u6570\u306e\u63a5\u7dda\u304c2\u6b21\u95a2\u6570\\(y=x^2\\)\u306b\u63a5\u3059\u308b\u6761\u4ef6\u306f, 2\u6b21\u95a2\u6570\u3068\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f<br>$$<br>\\left\\{ \\begin{aligned}y&amp;=x^2 \\\\[1.5ex] y&amp;=(3b^2+2b-1)x-2b^3-b^2-1\\end{aligned} \\right.<br>$$<br>\u304b\u3089\\(y\\)\u3092\u6d88\u53bb\u3057\u305f\\(x\\)\u306b\u95a2\u3059\u308b2\u6b21\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u6301\u3064\u3053\u3068\u3067\u3042\u308b. \\(y\\)\u3092\u6d88\u53bb\u3059\u308b\u3068, <br>$$<br>x^2=(3b^2+2b-1)x-2b^3-b^2-1<br>$$<br>\u3068\u306a\u308a, \\(x\\)\u306b\u95a2\u3057\u3066\u6574\u7406\u3059\u308b\u3068, <br>$$<br>x^2-(3b^2+2b-1)x+2b^3+b^2+1=0<br>$$<br>\u3068\u306a\u308a, \u3053\u308c\u304c\u91cd\u89e3\u3092\u6301\u3064\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f\u5224\u5225\u5f0f\u304c0\u306b\u306a\u308b\u3053\u3068\u3067, <br>$$<br>\\{-(3b^2+2b-1)\\}^2-4\\cdot 1\\cdot (2b^3+b^2+1)=0<br>$$<br>\u3067\u3042\u308b. \u5c55\u958b\u3057\u3066\u6574\u7406\u3059\u308b\u3068, <br>$$<br>9b^4+4b^3-6b^2-4b-3=0<br>$$<br>\u3068\u306a\u308a, \u3053\u308c\u306f1\u3064\u3081\u306e\u89e3\u6cd5\u3067\u5f97\u305f\\(b\\)\u306e4\u6b21\u65b9\u7a0b\u5f0f\u3068\u4e00\u81f4\u3059\u308b\u306e\u3067, \u540c\u69d8\u306b\u3057\u3066, \\(b=-1, 1\\)\u304c\u89e3\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b. \u3053\u308c\u304b\u3089\u6c42\u3081\u308b\u5171\u901a\u63a5\u7dda\u306f, <br>$$<br>y=0\\,\\,\\mbox{\u3068}\\,\\,y=4x-4<br>$$<br>\u306e2\u3064\u3067\u3042\u308b.<\/p>\n<\/div><\/div>\n\n\n\n<p>\u30b0\u30e9\u30d5\u3092\u66f8\u3044\u3066\u307f\u308b\u3068\u78ba\u304b\u306b2\u672c\u306e\u76f4\u7dda\u304c\u5171\u901a\u63a5\u7dda\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"641\" height=\"645\" src=\"https:\/\/math-friend.com\/wp-content\/uploads\/2025\/07\/045c2f154a7f0685160240cc593eda0d.png\" alt=\"\" class=\"wp-image-167\" srcset=\"https:\/\/math-friend.com\/wp-content\/uploads\/2025\/07\/045c2f154a7f0685160240cc593eda0d.png 641w, https:\/\/math-friend.com\/wp-content\/uploads\/2025\/07\/045c2f154a7f0685160240cc593eda0d-298x300.png 298w, https:\/\/math-friend.com\/wp-content\/uploads\/2025\/07\/045c2f154a7f0685160240cc593eda0d-150x150.png 150w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><\/figure>\n\n\n\n<p><br>\u4eca\u56de\u306f\\(b\\)\u306b\u95a2\u3059\u308b\u6761\u4ef6\u5f0f\u3092\u611a\u76f4\u306b\u5c55\u958b\u3057\u3066\\(b\\)\u306e4\u6b21\u65b9\u7a0b\u5f0f\u3092\u5f97\u307e\u3057\u305f\u304c, \u5404\u89e3\u6cd5\u3067\u5c11\u3057\u5de5\u592b\u3092\u3059\u308c\u30704\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304b\u306a\u3044\u65b9\u6cd5\u3082\u3042\u308a\u307e\u3059.<br><br>\u4f8b\u3048\u3070\u89e3\u6cd51\u3067\u306f\\(-(3b^2+2b-1)^2=-8b^3-4b^2-4\\)\u306e\u6761\u4ef6\u5f0f\u306b\u3066, \\(b=-1\\)\u3068\u3059\u308b\u3053\u3068\u3067\u4e21\u8fba\u304c\\(0\\)\u306b\u306a\u308b\u3053\u3068\u306b\u6c17\u4ed8\u3051\u3070, \u5c55\u958b\u524d\u306b\u4e21\u8fba\u3092\\((b+1)\\)\u3067\u304f\u304f\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3057, \u89e3\u6cd52\u3067\u306f\\(\\{-(3b^2+2b-1)\\}^2-4\\cdot 1\\cdot (2b^3+b^2+1)=0\\)\u306e\u5de6\u8fba\u306e2\u3064\u306e\u9805\u305d\u308c\u305e\u308c\u304c\\((b+1)\\)\u3067\u304f\u304f\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059. \u3053\u3061\u3089\u306e\u65b9\u304c\u5272\u308a\u7b97\u304c\u697d\u306b\u306a\u308b\u6c17\u306f\u3057\u307e\u3059\u304c, \u672c\u756a\u306e\u6975\u9650\u72b6\u614b\u3067\u3053\u306e\u4e8b\u5b9f\u306b\u6c17\u3065\u3051\u308b\u304b\u306f\u308f\u304b\u308a\u307e\u305b\u3093\u3057, \u611a\u76f4\u306b\u5c55\u958b\u3057\u3066\\(b\\)\u306e\u5024\u3092\u3044\u304f\u3064\u304b\u4ee3\u5165\u3057\u3066\u89e3\u304f\u65b9\u304c\u78ba\u5b9f\u3068\u3044\u3046\u8003\u3048\u3082\u3042\u308b\u304b\u3068\u601d\u3044\u307e\u3059\u306e\u3067\u306a\u3093\u3068\u3082\u8a00\u3048\u307e\u305b\u3093.<\/p>\n\n\n\n<p>youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/cj2jPliOLR0?si=H55XcHtLvZgXBRIF\" title=\"YouTube video player\" 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(2025 \u4e5d\u5dde\u5927\u5b66) 2\u6b21\u95a2\u6570\u30683\u6b21\u95a2\u6570\u306e\u5171\u901a\u63a5\u7dda\u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u3059. 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