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2017 USAMO Problems/Problem 6

Revision as of 20:40, 17 July 2017 by Justinjbd (talk | contribs) (→‎Solution)

Problem

Find the minimum possible value of

\[\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4},\]

given that $a,b,c,d,$ are nonnegative real numbers such that $a+b+c+d=4$.

Solution

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