The sum of a positive number and its reciprocal is thrice the difference of the number and its reciprocal. The number is :

A. $$\sqrt 2 $$

B. $$\frac{1}{{\sqrt 2 }}$$

C. $$\sqrt 3 $$

D. $$\frac{1}{{\sqrt 3 }}$$

Answer: Option A

Solution(By Examveda Team)

Let the number be x
Then,
$$\eqalign{ & \Leftrightarrow x + \frac{1}{x} = 3\left( {x - \frac{1}{x}} \right) \cr & \Leftrightarrow \frac{{{x^2} + 1}}{x} = 3\left( {\frac{{{x^2} - 1}}{x}} \right) \cr & \Leftrightarrow {x^2} + 1 = 3{x^2} - 3 \cr & \Leftrightarrow 2{x^2} = 4 \cr & \Leftrightarrow {x^2} = 2 \cr & \Leftrightarrow x = \sqrt 2 \cr} $$