Question

if a = 2 - root 3 find ( a - 1/a)3

Answer 1

$a = 2 + \sqrt{3} \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \frac{1}{a} = \frac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} } \\ \frac{1}{a} = \frac{2 - \sqrt{3} }{4 - 3} \\ \frac{1}{a} = \frac{2 - \sqrt{3} }{1} = 2 - \sqrt{3} \\ - \frac{ 1}{a} = - 2 + \sqrt{3} a - \frac{1}{a} \\ 2 + \sqrt{3} - 2 + \sqrt{3} \\ 2 \sqrt{3} \\ {(2 \sqrt{3} )}^{3} \\ 24 \sqrt{3}$