Question

Please help me to solve this

Answer 1

$\sqrt{x} - \frac{1}{ \sqrt{x} } \\ ( { \sqrt{x} - \frac{1}{ \sqrt{x} } )}^{2} = x + \frac{1}{x} - 2 \sqrt{x} \frac{1}{ \sqrt{x} } \\ = x + \frac{1}{x} - 2$
put value of x
$= ( \sqrt{2} - 1) + \frac{1}{ \sqrt{2} - 1} - 2 \\ = (\sqrt{2} - 1) + \frac{( \sqrt{2} + 1)}{( \sqrt{2} - 1)( \sqrt{2} + 1) } - 2 \\ = ( \sqrt{2} - 1) + ( \sqrt{2} + 1) - 2 \\ = \sqrt{2} - 2 \\ \sqrt{x} - \frac{1}{ \sqrt{x} } = \sqrt{ \sqrt{2 } - 2}$