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Home » The integers are 23, 24, and 25. - Dyverse

The integers are 23, 24, and 25. - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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- 30 = 9
Thus, the answer is $ \boxed{9} $.
Question: A science journalist analyzing a dataset finds that $ x + \f...
Solution: We are given $ x + \frac{1}{x} = 4 $. Square both sides:
\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} $.

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