Question

The sum of a 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. Both (A) and (B)

Answer 1

Answer: (D)

Both (A) and (B)

Let number be $n$ and $\frac{1}{n}$

According to the given condition,

$n+\frac{1}{n}=3(n-\frac{1}{n}$)

Or

$n+\frac{1}{n}=3n-\frac{3}{n}$

Or

$n^2+1=3n^2-3$

$3n^2-n^2=3+1$

$2n^2=4$

$\Rightarrow n=\pm \sqrt{2}$

Then reciprocal is $\pm \frac{1}{\sqrt{2}}$