Question

If a and b are two different positive real numbers, then which of the following relations is true

• A. $2\sqrt{ab}>(a+b)$
• B. $2\sqrt{ab}<(a+b)$
• C. $2\sqrt{ab}$ = $(a+b)$
• D. None of these

Answer 1

The correct option is B

$2\sqrt{ab}<(a+b)$

We know that A > G > H

Where A is arithmetic mean, G is geometric mean and H is harmonic mean, then A > G

$\Rightarrow \frac{a+b}{2}>\sqrt{ab}$ or (a + b) > 2$\sqrt{ab}$