Question 1
Prove that for every $x\gt 1$ there exists a triangle whose side lengths are $P_1(x)=x^4+x^3+2x^2+x+1$, $P_2(x)=2x^3+x^2+2x+1$, and $P_3(x)=x^4-1$. Prove that the largest angles of all these triangles are equal, and determine their common value.