If x=3+2sqrt2, x > 0, then the value of √(x)-1 over √(x) is :

If x=3+2sqrt2, x > 0, then the value of √(x)-1 over √(x)…

If ${{x=3+2\sqrt2,}}$ x > 0, then the value of $\sqrt x-{{1} \over \sqrt x}$ is :

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. 2.

Calculations:

${{x=3+2\sqrt2,}}$

Can be written as;

⇒ x = (√2)² + 1² + 2√2

⇒ x = (√2 + 1)²

⇒ √x = √2 + 1 and 1/√x = √2 - 1

Hence, the required value of $\sqrt x-{{1} \over \sqrt x}$

⇒ √2 + 1 - √2 + 1 = 2