TR-MO 2012 Problem 4

For all positive real numbers $x, y, z$ , show that $\frac{x(2x-y)}{y(2z+x)}+\frac{y(2y-z)}{z(2x+y)}+\frac{z(2z-x)}{x(2y+z)} \geq 1$ is true.

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.