Question

If x=2-√3,find the value of (x-1/3)cube

Answer 1

Hope u like my process
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$x = 2 - \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } = \frac{2 + \sqrt{3} }{(2 - \sqrt{3})(2 + \sqrt{3}) } \\ = \frac{2 + \sqrt{3} }{ {2}^{2} - {( \sqrt{3}) }^{2} } = \frac{2 + \sqrt{3} }{4 - 3} \\ = 2 + \sqrt{3} \\ \\ now.. \\ {(x + \frac{1}{x}) }^{3} \\ = (2 - \sqrt{3} + 2 + \sqrt{3} ) ^{3} \\ = {(4)}^{3} = 64$

Now for,

(x - 1/x)³
$\\ = (2 - \sqrt{3} - 2-\sqrt{3})^{3}\\ = ( -2 \sqrt{3})^{3} = - 24\sqrt{3}$
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Hope this is ur required answer

Proud to help you

Answer 2

(10-6√3)/27 just put all the value and solve it