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Home » From Beginners to Experts: Perfect ‘G’ in Cursive Fast—Watch Now! - jntua results

From Beginners to Experts: Perfect ‘G’ in Cursive Fast—Watch Now! - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 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.

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

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