Sum of First, Second, and Third Powers
Source: 1973 USAMO Problem 4
March 7, 2010
algebrapolynomialVietainequalitiescomplex numbersHi
Problem Statement
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*}