OIM 2005 Problem 1

Determine all triples of real numbers $(a,b,c)$ 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*}