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1. $x + \frac{1}{x} = 4$

Answer: Option A

Explanation:

x^{3} + \frac{1}{x^{3}} = (x + \frac{1}{x})^{3} - 3 x . \frac{1}{x} (x + \frac{1}{x}) = 4^{3} - 3 \times 4 = 64 - 12 = 52

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