Solve System
Source: 4-rd Czchech-Polish-Slovak Match, 2004
December 12, 2006
algebrasystem of equationsalgebra unsolved
Problem Statement
Solve in real numbers the system of equations: \begin{align*}
\frac{1}{xy}&=\frac{x}{z}+1 \\
\frac{1}{yz}&=\frac{y}{x}+1 \\
\frac{1}{zx}&=\frac{z}{y}+1 \\
\end{align*}