2017 USAMO Problems/Problem 6
Problem
Find the minimum possible value of
![\[\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4},\]](http://latex.artofproblemsolving.com/9/5/3/9530f2f6673410cf7229b9d8416c0a5c296467ae.png)
given that 
are nonnegative real numbers such that 
.
Solution
See here: https://artofproblemsolving.com/community/c5t211539f5h1434574_looks_like_mount_inequality_erupted_
or:
