Cyclic Fraction Extremes

Problem

Let $a, b, c, d \geqslant 0$ with $a + b + c + d = 4$ . Find the maximum and minimum values of

m = \frac{a}{b^3 + 4} + \frac{b}{c^3 + 4} + \frac{c}{d^3 + 4} + \frac{d}{a^3 + 4}.

Answer

Solution

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

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