Three-variable system
Source: Iberoamerican 2005
September 28, 2005
quadraticsalgebra unsolvedalgebra
Problem Statement
Determine all triples of real numbers such that \begin{eqnarray*} xyz &=& 8 \\ x^2y + y^2z + z^2x &=& 73 \\ x(y-z)^2 + y(z-x)^2 + z(x-y)^2 &=& 98 . \end{eqnarray*}