Minimum Sum of Positive Numbers with Fixed Product

Rarely Tested

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.

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