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Home » Divide by 2: \( y = \frac162 = 8 \). - Aurero

Divide by 2: \( y = \frac162 = 8 \). - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 \left(x + \frac{1}{x}\right)^2 = 4^2 = 16

📌 \Rightarrow x^2 + 2 + \frac{1}{x^2} = 16

📌 \Rightarrow x^2 + \frac{1}{x^2} = 14

📌 Now multiply both sides by 5:

📌 5x^2 + \frac{5}{x^2} = 5 \times 14 = 70

📌 Thus, the value is $ \boxed{70} $.

📌 Question: Compute the square of $ \sqrt{7 + 2\sqrt{10}} + \sqrt{7 - 2\sqrt{10}} $.

📌 Solution: Let $ x = \sqrt{7 + 2\sqrt{10}} + \sqrt{7 - 2\sqrt{10}} $. We compute $ x^2 $:

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