A Tangent-Line Bound

★ 6/10calculus Monotonicity AM-GM inequality

Problem

Let $a, b, c$ be positive real numbers with $a + b + c = 3$ . Prove that

\frac{a}{b^3+2} + \frac{b}{c^3+2} + \frac{c}{a^3+2} > \frac{5}{6}.

Answer

Solution

Difficulty	6/10
Topics	calculus, Monotonicity, AM-GM, inequality

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