KMO 2012 Problem 4

$a,b,c$ are positive numbers such that $a^2 + b^2 + c^2 = 2abc + 1$ . Find the maximum value of $(a-2bc)(b-2ca)(c-2ab)$

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.