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Home » You Won’t Guess Why Pear Engagement Rings Are Taking Over Dating Apps! - Databee Business Systems

You Won’t Guess Why Pear Engagement Rings Are Taking Over Dating Apps! - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \gcd(3^{15} - 1, 3^9 - 1) = 3^3 - 1 = 27 - 1 = 26.

📌 Therefore, the greatest common divisor is $oxed{26}$.**Question:** An archaeologist discovers an ancient Egyptian artifact with markings that represent two numbers \(x\) and \(y\), which are believed to encode a relationship through the equation: \[rac{x+y}{x-y} + rac{x-y}{x+y} = 3.\] Find all possible pairs \((x, y)\) of real numbers satisfying this equation.

📌 Solution:** Start with the given equation:

📌 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.

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