MathDB

6

Part of 1978 IMO Longlists

Problems(1)

Sides of triangle being polynomial functions

Source:

10/30/2010
Prove that for all X>1X > 1, there exists a triangle whose sides have lengths P1(X)=X4+X3+2X2+X+1,P2(X)=2X3+X2+2X+1P_1(X) = X^4+X^3+2X^2+X+1, P_2(X) = 2X^3+X^2+2X+1, and P3(X)=X4−1P_3(X) = X^4-1. Prove that all these triangles have the same greatest angle and calculate it.
algebrapolynomialfunctiontrigonometrygeometry unsolvedgeometry