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ambermole700Lv1
13 Apr 2020
Arithmetic-Geometric Mean Inequality If a1, a2, . . . , an are nonnegative numbers, then their arithmetic mean is
, and their geometric mean is
. The arithmetic-geometric mean inequality states that the geometric mean is always less than or equal to the arithmetic mean. In this problem we prove this in the case of two numbers x and y. Prove the arithmetic-geometric mean inequality
![](data:image/png;base64,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)
Arithmetic-Geometric Mean Inequality If a1, a2, . . . , an are nonnegative numbers, then their arithmetic mean is, and their geometric mean is
. The arithmetic-geometric mean inequality states that the geometric mean is always less than or equal to the arithmetic mean. In this problem we prove this in the case of two numbers x and y. Prove the arithmetic-geometric mean inequality
Patrina SchowalterLv2
24 May 2020