Question

if
$x = 2 - \sqrt{3 \: }$
find value of
${(x - \frac{1}{x}) }^{3}$

Answer 1

$x = 2 - \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 + \sqrt{3}$

Now,

${(x - \frac{1}{x}) }^{3} = {(2 - \sqrt{3} - 2 - \sqrt{3} ) }^{3} \\ \\ = {( - 2 \sqrt{3}) }^{3} \\ \\ = - 24 \sqrt{3}$

Answer 2

Heya buddy your answer is -24√3