{"id":2539,"date":"2025-08-07T14:00:00","date_gmt":"2025-08-07T05:00:00","guid":{"rendered":"https:\/\/math-friend.com\/?p=2539"},"modified":"2025-08-07T15:47:51","modified_gmt":"2025-08-07T06:47:51","slug":"%e3%80%90%e5%a4%a7%e9%98%aa%e5%85%ac%e7%ab%8b%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%91%e6%8c%87%e6%95%b0%e6%96%b9%e7%a8%8b%e5%bc%8f2025","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=2539","title":{"rendered":"\u3010\u5927\u962a\u516c\u7acb\u5927\u5b66\u3011\u6307\u6570\u3001\u5bfe\u6570\u3001\u4e09\u89d2\u95a2\u6570\u3001\u4e8c\u6b21\u95a2\u6570\u306e\u878d\u5408\u554f\u984c(2025)"},"content":{"rendered":"\n

\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n

\\(a\\)\u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b\u3068\u304d, \\(xy\\)\u5e73\u9762\u4e0a\u3067, \u4ee5\u4e0b\u306e\u6761\u4ef6$$
2^{-\\frac{1}{2}y}a^{2x}=2^{-\\frac{1}{2}(x^2+1)}
$$\u3092\u6e80\u305f\u3059\u70b9\\((x,y)\\)\u5168\u4f53\u3067\u4f5c\u3089\u308c\u308b\u56f3\u5f62\u3092\\(C\\)\u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.

(1) \\(C\\)\u306f\u653e\u7269\u7dda\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.
(2) \\(0<\\theta<\\pi\\)\u3068\u3059\u308b. \\(a=\\sin{\\theta}\\)\u3068\u3057\u305f\u3068\u304d\u306e, \u653e\u7269\u7dda\\(C\\)\u306e\u9802\u70b9\u306e\u5ea7\u6a19\u3092\\((s,t)\\)\u3068\u3059\u308b. \\(|s+t|\\leq 1\\)\u304c\u6210\u308a\u7acb\u3064\u3088\u3046\u306a\\(\\theta\\)\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.
(2025 \u5927\u962a\u516c\u7acb\u5927\u5b66 \u6587\u7cfb [2])<\/span><\/p>\n\n\n\n

\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n

\n

(1) \\(a>0\\)\u3088\u308a\u6761\u4ef6\u5f0f\u306e\u4e21\u8fba\u306f\u6b63\u3067\u3042\u308b\u304b\u3089, \u6761\u4ef6\u5f0f\u306e\u4e21\u8fba\u3067\u5e95\u3092\\(2\\)\u3068\u3059\u308b\u5bfe\u6570\u3092\u3068\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3042\u308b. \u307e\u305f, \u4e00\u822c\u306b\u6b63\u306e\u5b9f\u6570 \\(a\\neq 1\\), \\(p\\), \\(q\\)\u306b\u5bfe\u3057,
$$
p=q\\,\\,\\,\\iff\\,\\,\\,\\log_a{p}=\\log_a{q}
$$\u304c\u6210\u308a\u7acb\u3064\u304b\u3089, \u5bfe\u6570\u3092\u3068\u3063\u305f\u6761\u4ef6\u5f0f\u3082\u5143\u306e\u6761\u4ef6\u5f0f\u3068\u540c\u5024\u306b\u306a\u308b. \u3088\u3063\u3066,
$$
\\begin{align}
&2^{-\\frac{1}{2}y}a^{2x}=2^{-\\frac{1}{2}(x^2+1)}\\\\[1.5ex]
\\iff & \\log_2{2^{-\\frac{1}{2}y}a^{2x}}=\\log_2{2^{-\\frac{1}{2}(x^2+1)}}\\\\[1.5ex]
\\iff & -\\frac{1}{2}y+2x\\log_2{a}=-\\frac{1}{2}(x^2+1)\\\\[1.5ex]
\\iff & y=x^2+4\\left(\\log_2{a}\\right)x+1
\\end{align}
$$\u3068\u306a\u308a, \u3053\u308c\u306f\u653e\u7269\u7dda\u306e\u65b9\u7a0b\u5f0f\u306b\u4ed6\u306a\u3089\u306a\u3044.<\/p>\n\n\n\n

(2) \\(a=\\sin{\\theta}\\)\u3067\\(\\theta\\)\u306f\\(0<\\theta<\\pi\\)\u306e\u7bc4\u56f2\u3092\u52d5\u304f\u304b\u3089, \\(a\\)\u306f\\(0<a\\leq 1\\)\u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3053\u3068\u304c\u308f\u304b\u308b. \\(A=\\log_{2}{a}\\)\u3068\u304a\u304f\u3068, \\(0<a\\leq 1\\)\u3088\u308a, \\(A\\leq 0\\)\u3068\u306a\u308b. \u3053\u306e\u3068\u304d, (1)\u3067\u6c42\u3081\u305f\u653e\u7269\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f,
\\(\\displaystyle y=x^2+4Ax+1\\)\u3068\u306a\u308a, \u5e73\u65b9\u5b8c\u6210\u3059\u308b\u3068,
$$
y=(x+2A)^2-4A^2+1
$$\u3068\u306a\u308b. \u3053\u308c\u304b\u3089, $$
s=-2A,\\,\\,\\,t=-4A^2+1
$$\u3068\u8868\u305b\u308b. \\(\\displaystyle |s+t|\\leq 1\\)\u306f, $$
\\begin{align}
&|-2A-4A^2+1|\\leq 1\\\\[1.5ex]
\\iff & |4A^2+2A-1|\\leq 1
\\end{align}
$$\u3068\u306a\u308b\u306e\u3067, \u3053\u306e\u4e0d\u7b49\u5f0f\u3092\\(A\\)\u306b\u3064\u3044\u3066\u89e3\u304f\u3053\u3068\u3067, \u6700\u7d42\u7684\u306b\\(\\theta\\)\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3066\u3044\u304f.

$$
\\begin{align}
&|4A^2+2A-1|\\leq 1\\\\[1.5ex]
\\iff & -1\\leq 4A^2+2A-1\\leq 1\\\\[1.5ex]
\\iff & -1\\leq 4A^2+2A-1\\,\\,\\,\u304b\u3064\\,\\,\\,4A^2+2A-1\\leq 1\\\\[1.5ex]
\\iff & 4A\\left(A+\\frac{1}{2}\\right)\\geq 0\\,\\,\\,\u304b\u3064\\,\\,\\,2A^2+A-1\\leq 0\\\\[1.5ex]
\\iff & \u300cA\\leq -\\frac{1}{2}\\,\\,\\,\u307e\u305f\u306f\\,\\,\\,A\\geq 0\u300d\\,\\,\\,\u304b\u3064\\,\\,\\, (2A-1)(A+1)\\leq 0\\\\[1.5ex]
\\iff & \u300cA\\leq -\\frac{1}{2}\\,\\,\\,\u307e\u305f\u306f\\,\\,\\,A\\geq 0\u300d\\,\\,\\,\u304b\u3064\\,\\,\\, -1\\leq A\\leq \\frac{1}{2}\\\\[1.5ex]
\\iff & -1\\leq A\\leq -\\frac{1}{2} \\,\\,\\,\u307e\u305f\u306f\\,\\,\\,0\\leq A\\leq \\frac{1}{2}
\\end{align}
$$\u3068\u306a\u308b. \u3057\u304b\u3057, \u524d\u63d0\u306e\\(A\\leq 0\\)\u304b\u3089, \\(A\\)\u306e\u7bc4\u56f2\u306f,
$$
-1\\leq A\\leq -\\frac{1}{2} \\,\\,\\,\u307e\u305f\u306f\\,\\,\\,A=0
$$\u3068\u306a\u308b.

\\(\\displaystyle A=\\log_2{a}\\)\u3060\u3063\u305f\u306e\u3067, \u3053\u308c\u306f,
$$
\\begin{align}
&-1\\leq \\log_2{a}\\leq -\\frac{1}{2} \\,\\,\\,\u307e\u305f\u306f\\,\\,\\,\\log_2{a}=0\\\\[1.5ex]
\\iff &2^{-1}\\leq a \\leq 2^{-\\frac{1}{2}}\\,\\,\\,\u307e\u305f\u306f\\,\\,\\,a=1\\\\[1.5ex]
\\iff &\\frac{1}{2}\\leq a \\leq \\frac{1}{\\sqrt{2}}\\,\\,\\,\u307e\u305f\u306f\\,\\,\\,a=1\\\\[1.5ex]
\\end{align}
$$\u3068\u306a\u308b.

\u3055\u3089\u306b, \\(a=\\sin{\\theta}\\)\u3068\u7f6e\u3044\u3066\u3044\u305f\u306e\u3067, \u554f\u984c\u3067\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\\(\\theta\\)\u306e\u7bc4\u56f2\\(0<\\theta<\\pi\\)\u3092\u524d\u63d0\u3068\u3057\u3066, \u3053\u308c\u306f,
$$
\\begin{align}
&\\frac{1}{2}\\leq \\sin{\\theta} \\leq \\frac{1}{\\sqrt{2}}\\,\\,\\,\u307e\u305f\u306f\\,\\,\\,\\sin{\\theta}=1\\\\[1.5ex]
\\iff & \\frac{\\pi}{6}<\\theta < \\frac{\\pi}{4} \\,\\,\\, \u307e\u305f\u306f\\,\\,\\,\\frac{3\\pi}{4}<\\theta<\\frac{5\\pi}{6}\\,\\,\\,\u307e\u305f\u306f\\,\\,\\,\\theta=\\frac{\\pi}{2}
\\end{align}
$$\u3068\u306a\u3063\u3066, \u3053\u308c\u304c\u6c42\u3081\u308b\\(\\theta\\)\u306e\u7bc4\u56f2\u3067\u3042\u308b.
<\/p>\n<\/div><\/div>\n\n\n\n

youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n