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1. $x + \frac{1}{x} = \sqrt{3}$

Answer: Option A

Explanation:

∴ x^{3} + \frac{1}{x^{3}} = {(x + \frac{1}{x})}^{3} - 3 . x . \frac{1}{x} (x + \frac{1}{x}) = {(\sqrt{3})}^{3} - 3 . \sqrt{3} = 3 \sqrt{3} - 3 \sqrt{3} = 0

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