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Function

$$F(x_1,x_2,...,x_n) = \sum_{i=1}^n x_i$$

on the constraint

$$G(x_1,x_2,...,x_n)=\prod_{i=1}^n x_i-1$$

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1 Answer 1

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The inequality of arithmetic and geometric means says:

$(x_1x_2....x_n)^{1/n} \le \frac{F(x_1,...,x_n)}{n}$.

If $x_1x_2....x_n=1$, then we get

$n=F(1,...,1) \le F(x_1,...,x_n)$.

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  • $\begingroup$ thank you so much, Fred! $\endgroup$
    – 2Napasa
    Sep 23, 2021 at 7:57

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