An Asymmetric Bound

★ 8/10Substitution algebra AM-GM inequality

Problem

Let $a, b, c > 0$ with $ab + bc + ca = 1$ . Prove that

\frac{2}{a^2+1} + \frac{2}{b^2+1} + \frac{3}{c^2+1} \le \frac{16}{3}.

Answer

Solution

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

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