I want to solve the following three equations for $x,y,z$:
$$\begin{eqnarray}k_1&=&\frac{x+y+z}{yz}\\ k_2&=&\frac{x^2+y^2+z^2}{y^2z^2}\\ k_3&=&\frac{x^3+y^3+z^3}{y^3z^3}\end{eqnarray}$$
where $k_1,k_2,k_3$ are constants.
Is there any kind of standard methods?