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Home » We know that \(S = 54\pi\), so: - Dachbleche24

We know that \(S = 54\pi\), so: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 a^2 + b^2 = b^2(x^2 + 1), \quad a^2 - b^2 = b^2(x^2 - 1)

📌 So the expression becomes:

📌 \frac{b^2(x^2 + 1)}{b^2(x^2 - 1)} + \frac{b^2(x^2 - 1)}{b^2(x^2 + 1)} = \frac{x^2 + 1}{x^2 - 1} + \frac{x^2 - 1}{x^2 + 1}

📌 Let $ y = \frac{x^2 + 1}{x^2 - 1} $, then the expression becomes:

📌 y + \frac{1}{y}

📌 We compute $ y + \frac{1}{y} $. First, recall that $ x + \frac{1}{x} = 5 $. Square both sides:

📌 x^2 + 2 + \frac{1}{x^2} = 25 \Rightarrow x^2 + \frac{1}{x^2} = 23

📌 Now compute $ x^2 + 1 $ and $ x^2 - 1 $:

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