IMO 1978 LL CUB6

Prove that for all X > 1 there exists a triangle whose sides

imolonglistmathematicsolympiad

IMO 1978 LL CUB6

Origin: CUB

Problem

Prove that for all X > 1 there exists a triangle whose sides have lengths P1(X) = X4+X3+2X2+X+1, P2(X) = 2X3+X2+2X+1, and P3(X) = X4−1. Prove that all these triangles have the same greatest angle and calculate it.