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Sides of triangle being polynomial functions

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October 30, 2010
algebrapolynomialfunctiontrigonometrygeometry unsolvedgeometry

Problem Statement

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.
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