Question

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

• A. $2\surd \left(ab\right)>(a+b)$
• B. $2\surd \left(ab\right)<(a+b)$
• C. $2\surd \left(ab\right)=(a+b)$
• D. None of these

Answer 1

The correct option is B

$2\surd \left(ab\right)<(a+b)$

Explanation for the correct option:

As we know, $AM\ge GM$

$\Rightarrow \frac{(a+b)}{2}\ge \surd \left(ab\right)$

$\Rightarrow (a+b)\ge 2\surd \left(ab\right)$

Hence, Option ‘B’ is Correct.