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Show x³y+y³z+z³x is a constant

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,812
Show that for all real numbers $x,\,y,\,z$ such that $x+y+z=0$ and $xy+yz+zx=-3$, the expression $x^3y+y^3z+z^3x$ is a constant.