Question

If x = 1-underoot 2 then find the value of x-1/x

Answer 1

$given \: \: x = 1 - \sqrt{2} \\ \frac{1}{x} = \frac{1}{1 - \sqrt{2}} = \frac{1 + \sqrt{2}}{(1 - \sqrt{2})(1 + \sqrt{2})} \\ = \frac{1 + \sqrt{2}}{1 - 2} = - (1 + \sqrt{2} ) \\ \\ x - \frac{1}{x} = (1 - \sqrt{2} ) + (1 + \sqrt{2} ) = 2$