ILL 1978 Problem 6

Prove that for all $X > 1$ , there exists a triangle whose sides have lengths $P_1(X) = X^4+X^3+2X^2+X+1, P_2(X) = 2X^3+X^2+2X+1$ , and $P_3(X) = X^4-1$ . Prove that all these triangles have the same greatest angle and calculate it.