Question 6
Find the minimum of
$$\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4}$$
for $a,b,c,d\ge0$ with $a+b+c+d=4$.
Proposed by Titu Andreescu. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.
$$\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4}$$
for $a,b,c,d\ge0$ with $a+b+c+d=4$.
Proposed by Titu Andreescu. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.