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📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 rac{x+y}{x-y} + rac{x-y}{x+y} = 3.

📌 Let \( u = rac{x+y}{x-y} \), so the second term becomes \( rac{1}{u} \). Then the equation becomes:

📌 u + rac{1}{u} = 3.

📌 Multiply both sides by \(u\) (assuming \(u

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

📌 u = rac{3 \pm \sqrt{9 - 4}}{2} = rac{3 \pm \sqrt{5}}{2}.

📌 So \( u = rac{3 + \sqrt{5}}{2} \) or \( u = rac{3 - \sqrt{5}}{2} \).

📌 Now recall \( u = rac{x+y}{x-y} \). Let \( r = rac{x}{y} \), assuming \(y

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