PL-OM 2020 Problem 1

Assume that for pairwise distinct real numbers $a,b,c,d$ holds: $(a^2+b^2-1)(a+b)=(b^2+c^2-1)(b+c)=(c^2+d^2-1)(c+d).$ Prove that $a+b+c+d=0.$

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.