Track / Stage 4 / 259 of 340 #519 of 1964

Derive the inequality between the arithmetic mean and the geometric mean from Muirhead's inequality (problem 61424).

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This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

I solved it I didn't Skip

Official solution

According to Muirhead's inequality $x_{1}^{n}+\ldots+x_{n}^{n} \geq n x_{1} \ldots x_{n}$.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.