AM-GM inequality for n non-negative numbers for JEE

Formula

\(\frac{x_1+x_2+\cdots+x_n}{n}\ge (x_1x_2\cdots x_n)^{1/n}\)

Variables: \(x_1,x_2,\dots,x_n\): non-negative real numbers.

Conditions: All \(x_i\ge 0\); equality iff \(x_1=x_2=\cdots=x_n\).

General inequality problems, optimization, symmetric expressions.