Question

please answer this question
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Answer 1

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

By cubing both the sides,in the above equation,we get----

$( {x} + \frac{1}{x} )^{3} = ({ \sqrt{3} )}^{3}$

${x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} ) = 3 \sqrt{3}$

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

${x}^{3} + \frac{1}{ {x}^{3} } = 3 \sqrt{3} - 3 \sqrt{3}$

${x}^{3} + \frac{1}{ {x}^{3} } = 0$