Q. If 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) $\frac{A^{2}}{G^{2}}$
C) $\frac{A}{G^{2}}$
D) $\frac{G}{A^{2}}$
Explanation
(a)
Let the two numbers be a and b, then
$A = \frac{a + b}{2},G = \sqrt{ab,}$ H=$\ \ \frac{2ab}{a + b}$
$\Rightarrow H = \frac{ab}{A} \Rightarrow H = \frac{G^{2}}{A}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.