Problem

Source: 1973 USAMO Problem 4

Tags: algebra, polynomial, Vieta, inequalities, complex numbers, Hi



Determine all roots, real or complex, of the system of simultaneous equations \begin{align*} x+y+z &= 3, \\ x^2+y^2+z^2 &= 3, \\ x^3+y^3+z^3 &= 3.\end{align*}