In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same. The simplest non-trivial case — i.e., with more than one variable — for two non-negative numbers x and y, is the statement that Extensions of the AM–GM inequality are available to include or generalized means.
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