2 equations, 3 variables
Source: Canada 2003
March 5, 2006
algebra unsolvedalgebra
Problem Statement
Find all real positive solutions (if any) to
\begin{align*}
x^3+y^3+z^3 &= x+y+z, \mbox{ and} \\
x^2+y^2+z^2 &= xyz.
\end{align*}
Source: Canada 2003