Question

if X equals to 1 minus root 2 find the value of x - 1/ X the whole cube

Answer 1

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$= > \: \: \: x = 1 - \sqrt{2 } \\ \\ = > \: \: \: \: \frac{1}{x} = \frac{1}{1 - \sqrt{2} } = \frac{(1 + \sqrt{2}) }{(1 - \sqrt{2} )(1 + \sqrt{2} )} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1 + \sqrt{2} }{ {1}^{2} - {( \sqrt{2}) }^{2} } = \frac{1 + \sqrt{2} }{1 - 2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - (1 + \sqrt{2} ) = - 1 - \sqrt{2}$
Now,
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$= > \: \: {(x - \frac{1}{x}) }^{3} \\ \\ =( (1 - \sqrt{2} ) - ( - 1 - \sqrt{2} )) ^{3} \\ \\ = {(1 - \sqrt{2} + 1 + \sqrt{2}) }^{3} \\ \\ = {(2)}^{3} \\ \\ = 8.......answer...$
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Hope this is ur required answer

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