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I Love You in French: The Perfect Phrase That’ll Make Your Website Rank #1 in Romance - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Therefore, the solutions are all real pairs where \( x = \sqrt{5} y \) or \( x = -\sqrt{5} y \), \( y

📌 e 0 \). However, since the equation is symmetric in \((x,y)\) under this proportionality and no restriction on sign, the solution set is:

📌 oxed{(x, y) ext{ such that } x = \pm \sqrt{5} y, \; y

📌 Question:** A historian analyzing a manuscript finds an expression involving complex numbers \( z \) and \( w \) satisfying \[ rac{z + w}{z - w} + rac{z - w}{z + w} = 2. \] Determine the value of \( \left| rac{z}{w}

📌 ight| \), assuming \( w

📌 e 0 \) and \( z, w \in \mathbb{C} \).

📌 Solution:** Let \( u = rac{z + w}{z - w} \), so the second term is \( rac{1}{u} \), and the equation becomes:

📌 u + rac{1}{u} = 2.

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