Relation Between AM, GM and HM

Relation Between AM, GM and HM

## Formula

For two positive numbers:

$$AM=\frac{a+b}{2}$$

$$GM=\sqrt{ab}$$

$$HM=\frac{2ab}{a+b}$$

The fundamental relation is:

$$AM\ge GM\ge HM$$

Equality holds when:

$$a=b$$

## Usage

- Used to compare different means and solve inequality-based questions.