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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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V.19 Inequalities

Let x and y be two nonnegative real numbers. Then (Image - Image)2 = x + y - 2Image is a nonnegative real number,from which it follows that Image(x + y) ≤ ImageThat is, the arithmetic mean of x and y is at least as big as the geometric mean. This conclusion ...

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