A Cyclic Product Below 1

★ 8/10Substitution algebra AM-GM inequality

Problem

Let $a, b, c > 0$ with $abc = 1$ . Prove that

\left(a - 1 + \frac1b\right)\left(b - 1 + \frac1c\right)\left(c - 1 + \frac1a\right) \le 1.

Answer

Solution

Difficulty	8/10
Topics	Substitution, algebra, AM-GM, inequality

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