Question

a=1-root 2
Find = (a-1/a) cube
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Answer 1

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

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

$( \frac{ \sqrt{2}( \sqrt{2} + 1) }{ \sqrt{2} - 1( \sqrt{2} + 1} {)}^{3}$

$\frac{2 \sqrt{2}( \sqrt{2} + 1 {)}^{2} }{(2 - 1)}$

$2 \sqrt{2} ( \sqrt{2} {)}^{3} + {1}^{3} + 3 \sqrt{2} ( \sqrt{2} + 1)$

$2 \sqrt{2} (2 \sqrt{2} + 1 + 6 + 3 \sqrt{2}$

$2( \sqrt{2} (5 \sqrt{2} + 7)$

$20 + 14 \sqrt{2}$

Thanks