Art of Problem Solving

Mock AIME 2 2006-2007 Problems/Problem 11

Problem

Find the sum of the squares of the roots, real or complex, of the system of simultaneous equations

$x+y+z=3, x^2+y^2+z^2=3,x^3+y^3+z^3 =3.$

Problem Source

This problem was given to 4everwise by a friend, Henry Tung. Upper classmen bullying freshmen. (Just kidding; it's a nice problem. )