Minimum Sum of Positive Numbers with Fixed Product
If:
$$x_1x_2\cdots x_n=P$$
then:
$$x_1+x_2+\cdots+x_n\geq n\sqrt[n]{P}$$
Equality occurs when:
$$x_1=x_2=\cdots=x_n=\sqrt[n]{P}$$
Usage
- Used for direct optimization of sums under a fixed-product condition.