SE-SKOLORNAS 2013 Problem 6

Let $a, b, c$ , be real numbers such that $a^2b^2 + 18 abc > 4b^3+4a^3c+27c^2 .$ Prove that $a^2>3b$ .

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.