Question

If the arithmetic mean of two positive numbers is $A$, their geometric mean is $G$ and harmonic mean is $H$, then $H$is equal to

• A. $\frac{G^2}{A}$
• B. $\frac{G}{A^2}$
• C. $\frac{A^2}{G^2}$
• D. $\frac{A}{G^2}$

Answer 1

The correct option is A

$\frac{G^2}{A}$

Find the value of the harmonic mean $H$:

Given that the arithmetic mean of two positive numbers is $A$, their geometric mean is $G$ .

Let $a$ and $b$ be two numbers.

The arithmetic mean (AM) $A=\frac{(a+b)}{2}$

The geometric mean (GM)$G=\sqrt{ab}$

The harmonic mean (HM) $H=\frac{2ab}{(a+b)}$

$=\frac{G^2}{A}$

Hence, the correct option is A.