AM-GM inequality

The arithmetic mean–geometric mean (AM–GM) inequality states that for positive real numbers $x_1$, $x_2$, …, $x_n$, $\frac{1}{n}\sum_{i=1}^{n} x_{i} \geq \Bigl(\prod_{i=1}^{n} x_{i}\Bigr)^{\frac{1}{n}},$ that is, the arithmetic mean of a set is always greater than or equal to its geometric mean, with equality if and only if all of the $x_i$ are equal.

For example, the case $n=2$ states that if we have two positive numbers $x$ and $y$, they satisfy: $\frac{x+y}{2} \geq \sqrt{\vphantom{()}x y}$ with equality if and only if $x=y$.