Question

 if x = 1-√2 find the value of x -1/ x​

Answer 1

Answer:

$x = 1 - \sqrt{2} \\ \\ x - \frac{1}{x} = 1 - \sqrt{2 } - \frac{1}{1 - \sqrt{2} } \\ \\ \frac{1 - \sqrt{2} \times 1 - \sqrt{2} - 1 }{1 - \sqrt{2} } \\ \\ = \frac{1 - \sqrt{2} - \sqrt{2} + 2 - 1}{ 1- \sqrt{2} } \\ \\ = \frac{1 - \sqrt{4} + 1}{1 - \sqrt{2} } = \frac{ \sqrt{4} }{1 - \sqrt{2} } = \frac{2}{1 - \sqrt{2} }$