Reversed Cyclic Fractions

Problem

Let $a, b, c > 0$ with $a + b + c = 3$ . Prove that

\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \leqslant \frac{a}{b^2} + \frac{b}{c^2} + \frac{c}{a^2}.

Answer

Solution

Difficulty	7/10
Topics	Substitution, algebra, inequality

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