MathDB
x^3y+ y^3z+z^3x is constant, when x + y + z = 0 and xy + yz + zx = -3

Source: CRMO 2012 Region 2 p6

September 30, 2018
algebraidentityalgebraic identities

Problem Statement

Show that for all real numbers x,y,zx,y,z such that x+y+z=0x + y + z = 0 and xy+yz+zx=āˆ’3xy + yz + zx = -3, the expression x3y+y3z+z3xx^3y + y^3z + z^3x is a constant.