AT-OEMO-BEG 2009 Problem 2

Let $x$ and $y$ be nonnegative real numbers. Prove that $(x +y^3) (x^3 +y) \ge 4x^2y^2$ . When does equality holds?

(Task committee)

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.