ABC26GN1676 · Problems on Numbers
Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
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
Explanation
Let the number be $x$. Then, $x+\frac{1}{x}=3\left(x-\frac{1}{x}\right)$ $$\begin{aligned} & \Leftrightarrow \frac{x^{2}+1}{x}=3\left(\frac{x^{2}-1}{x}\right) \\ & \Leftrightarrow x^{2}+1=3 x^{2}-3 \\ & \Leftrightarrow 2 x^{2}=4 \\ & \Leftrightarrow x^{2}=2 \\ & \Leftrightarrow x=\sqrt{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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