Question

The sum of any positive number and its reciprocal is always greater than or equal to

• A. 5
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

Let the positive number be x.
So, its reciprocal will be $\frac{1}{x}$
We know that the arithmetic mean of two numbers is always greater than or equal to its geometric mean.
$\therefore \frac{x+\frac{1}{x}}{2}\ge x\times \frac{1}{x}$
$\Rightarrow \frac{x+\frac{1}{x}}{2}\ge 1$
$\Rightarrow x+\frac{1}{x}\ge 2$
Thus, the sum of any positive number and its reciprocal is always greater than or equal to 2.
Hence, the correct answer is option (2).