MEMO 2012 T1

Find all triplets $(x,y,z)$ of real numbers such that $2x^3 + 1 = 3zx$ $2y^3 + 1 = 3xy$ $2z^3 + 1 = 3yz$

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.