ZA-SAMO 2008 Problem 3

Let $a,b,c$ be positive real numbers. Prove that $(a+b)(b+c)(c+a)\ge 8(a+b-c)(b+c-a)(c+a-b)$ and determine when equality occurs.

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.