SMO 2009 Problem 4

find largest constant C st $\sum_{i=1}^{4} (x_i+1/x_i)^3 \geq C$ for all positive real numbers $x_1,..,x_4$ st $x_1^3+x_3^3+3x_1x_3=x_2+x_4=1$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.