Question

x=3+2√2,then find the value of √x-1/√x

Answer 1

$\textbf{ Hello Mate! }$

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

$\boxed{ Answer : 2 }$

Hope it helps