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
Solution
We take note of the obvious solution: (1,1,1). Now we manipulate the equations a bit:
Therefore, x, y, and z are the roots of
Therefore, the only solution to those three equations is (1,1,1). The sum of the squares of the roots is
Problem Source
This problem was given to 4everwise by a friend, Henry Tung. Upper classmen bullying freshmen. (Just kidding; it's a nice problem. )