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Home » Won’t You Step Into My House? Inside My Perfect, Warm Welcome Awaits! - Groen Casting

Won’t You Step Into My House? Inside My Perfect, Warm Welcome Awaits! - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 したがって、\(\sin^4 x + \cos^4 x\) の最小値は \(\boxed{\frac{1}{2}}\) です。

📌 問題: 点 \((1, 2)\) に最も近い直線 \(y = 2x + 3\) 上の点を求めよ。

📌 解: 直線 \(y = 2x + 3\) 上の点 \((1, 2)\) に最も近い点を見つけるには、点から直線までの垂直距離を最小化する必要があります。直線 \(y = 2x + 3\) の傾きは 2 なので、垂直な直線の傾きは \(-\frac{1}{2}\) です。

📌 点 \((1, 2)\) を通り傾き \(-\frac{1}{2}\) の直線の式は次のとおりです:

📌 y - 2 = -\frac{1}{2}(x - 1)

📌 y - 2 = -\frac{1}{2}x + \frac{1}{2} \implies y = -\frac{1}{2}x + \frac{5}{2}

📌 この直線と \(y = 2x + 3\) の交点を見つけるために、方程式を等しくします:

📌 2x + 3 = -\frac{1}{2}x + \frac{5}{2}

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