Question

If $x=3-2\sqrt{2}$, then the value of $\sqrt{x}-\frac{1}{\sqrt{x}}$ is

• A. $\sqrt{2}$
• B. $-\sqrt{2}$
• C. $1$
• D. $-2$

Answer 1

The correct option is D $-2$

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