Question

For a set of positive numbers, the product $AM\times HM$ will be equal to:(AM, GM and HM are Arithematic mean, Geometric mean and Harmonic mean)

• A. $G{M}^2$
• B. $G{M}^3$
• C. $2G{M}^2$
• D. $GM$

Answer 1

Answer: (A)

$G{M}^2$

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

Arithmetic mean $=\frac{a+b}{2}$

Geometric mean $=\sqrt{ab}$

Harmonic mean $=\frac{2ab}{a+b}$

$AM\times HM=\frac{a+b}{2}\times \frac{2ab}{a+b}=ab=(GM{)}^2$

$AM\times HM=(GM{)}^2$