A Product Bounded by One-Eighth

★ 6/10Substitution algebra AM-GM inequality

Problem

Let $x, y, z > 1$ with

\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 2.

Prove that

8(x-1)(y-1)(z-1) \leqslant 1.

Answer

Solution

Difficulty	6/10
Topics	Substitution, algebra, AM-GM, inequality

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