Question

The lengths of two line segments are $a$ units and $b$ units respectively. Then the correct relation between them is

• A. $\frac{(a+b)}{2}>\sqrt{ab}$
• B. $\frac{(a+b)}{2}<\sqrt{ab}$
• C. $\frac{(a+b)}{2}=\sqrt{ab}$
• D. $\frac{(a+b)}{2}\le \sqrt{ab}$
• E. $\frac{(a+b)}{2}\ge \sqrt{ab}$

Answer 1

The correct option is E $\frac{(a+b)}{2}\ge \sqrt{ab}$

For $a\ne b$, Arithmetic $Mean>GeometricMean$. For $a=b$,
$ArithmeticMean=GeometricMean$.
$\therefore (a+b)/2\ge \sqrt{ab}$.