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Home » The arc length \( L \) is given by: - Belip

The arc length \( L \) is given by: - Belip

📅 May 7, 2026 👤 scraface

May 07, 2026

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📌 rac{a + b}{a - b} + rac{a - b}{a + b} = 3

📌 Let \( u = rac{a + b}{a - b} \), then the expression is \( u + rac{1}{u} = 3 \). Multiply both sides by \( u \):

📌 u^2 + 1 = 3u \Rightarrow u^2 - 3u + 1 = 0

📌 So \( rac{a + b}{a - b} = rac{3 \pm \sqrt{5}}{2} \). Letâs take one root (both valid due to symmetry). Set:

📌 rac{a + b}{a - b} = rac{3 + \sqrt{5}}{2}

📌 2(a + b) = (3 + \sqrt{5})(a - b)

📌 2a + 2b = (3 + \sqrt{5})a - (3 + \sqrt{5})b

📌 2a - (3 + \sqrt{5})a + 2b + (3 + \sqrt{5})b = 0

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