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$I f x = 3 + 2 \sqrt{2}, t h e n t h e v a l u e o f \sqrt{x} - \frac{1}{\sqrt{x}} i s :$

A. 1

B. 2

C. $2 \sqrt{2}$

D. $3 \sqrt{3}$

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Correct Answer : B.

{(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} = x + \frac{1}{x} - 2

= (3 + 2 \sqrt{2}) + \frac{1}{(3 + 2 \sqrt{2})} - 2

= (3 + 2 \sqrt{2}) + \frac{1}{(3 + 2 \sqrt{2})} \times \frac{(3 - 2 \sqrt{2})}{(3 - 2 \sqrt{2})} - 2

= (3 + 2 \sqrt{2}) + (3 - 2 \sqrt{2}) - 2

= 4.

∴ (\sqrt{x} - \frac{1}{\sqrt{x}}) = 2 .

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