Question

pls solve this question

Answer 1

${(x + \frac{1}{x} )}^{2} \\ = {x}^{2} + \frac{1}{ {x}^{2} } + 2.x. \frac{1}{x} \\ = 7 + 2 \\ = 9$

Therefore,

$x + \frac{1}{x} = \sqrt{9} = 3$

Now,

${(x + \frac{1}{x}) }^{3} = {(3)}^{3} \\ = > {x}^{3} + \frac{1}{ {x}^{3} } + 3.x. \frac{1}{x} (x + \frac{1}{x} ) = 27 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 3 = 27 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = 27 - 9 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = 18$