Product bound from fixed sum by AM-GM for JEE

Formula

\(x_1x_2\cdots x_n\le \left(\frac{x_1+x_2+\cdots+x_n}{n}\right)^n\)

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

Conditions: All \(x_i\ge 0\); equality iff all are equal.

Maximizing product for given sum.