Three Radicals, At Least Nine

★ 7/10Substitution algebra AM-GM inequality

Problem

Let $x, y, z$ be positive reals with $xyz = 1$ . Prove that

\sqrt{1 + 8x} + \sqrt{1 + 8y} + \sqrt{1 + 8z} \geqslant 9.

Answer

Solution

Difficulty	7/10
Topics	Substitution, algebra, AM-GM, inequality

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