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

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Question

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

Options:

A . $$\sqrt 2 $$

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

C . $$\sqrt 3 $$

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

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

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