Question

if
$x - \frac{1}{x} = 2 \sqrt{3}$
find the value of
${x}^{3} - \frac{1}{ {x}^{3} }$
​

Answer 1

$x - \frac{1}{x} = 2 \sqrt{3} \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = ( {x - \frac{1}{x} })^{3} + 3(x - \frac{1}{x} ) \\ {x}^{3} - \frac{1}{ {x}^{3} } = ( {2 \sqrt{3} })^{3} + 3 \times 2 \sqrt{3} \\ = 24 \sqrt{3} + 6 \sqrt{3} \\ = 30 \sqrt{3}$