Question

please tell me the answer of the question in the given photo.plz send the answer fast with the steps

Answer 1

x= 1- root2
1/x = 1/1- root2 * 1+ root2/ 1+ root2
= 1 +root2/ (1)^2 - (root2) ^2
1+ root2 / 1 - 2
1 + root2/ -1
1/x = -(1 +root2)
x-1/x = 1-root2+1+root2
x-1/x =2
(x-1/x)^3 = (2)^3 =8 is the answer

Answer 2

Hope u like my process
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$= > x = 1 - \sqrt{2} \\ \\ = > \frac{1}{x} = \frac{1}{1 - \sqrt{2} } = \frac{(1 + \sqrt{2}) }{(1 - \sqrt{2} )(1 + \sqrt{2} )} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1 + \sqrt{2} }{ {1}^{2} - {( \sqrt{2} )}^{2} } = \frac{1 + \sqrt{2} }{1 - 2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = - (1 + \sqrt{2} ) = - 1 - \sqrt{2}$
$= > {(x - \frac{1}{x} )}^{3} \\ \\ = {((1 - \sqrt{2}) - ( - 1 - \sqrt{2} ) }^{3} \\ \\ = {(1 - \sqrt{2} + 1 + \sqrt{2} )}^{3} \\ \\ = { (2) }^{3} = 8$
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Hope this is ur required answer

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