If a and b are two different positive real numbers, then which of th

Question -

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

Options:

A .

2 \sqrt{a b} > (a + b)

B .

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

C .

2 \sqrt{a b}

(a + b)

D . None of these

Answer: Option B
:
B

We know that A > G > H

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

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

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