Question

if x = 1 - √2, find the value of (x-1/X)³​

Answer 1

Answer: 1/2

Step-by-step explanation: Two numbers r and s sum up to \frac{1}{2} exactly when the average of the two numbers is \frac{1}{2}*\frac{1}{2} = \frac{1}{4}

Answer 2

$x = 1 + \sqrt{2}$

$\\ now$

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

$\\ = > [1 + \sqrt{2} - ( \frac{1}{ \sqrt{2 } + 1 } ) \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1} ) {]}^{3}$

$\\ = > [ 1 + \sqrt{2 } - ( \sqrt{2} - 1) {]}^{3}$

$\\ = > (1 + \sqrt{2} - \sqrt{2} + 1 {)}^{3} = {2}^{3} = 8$

I hope this will help you dear..

Always stay safe and stay healthy..