MathDB

1

Part of 2005 IberoAmerican

Problems(1)

Three-variable system

Source: Iberoamerican 2005

9/28/2005
Determine all triples of real numbers (a,b,c)(a,b,c) 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*}
quadraticsalgebra unsolvedalgebra