Solve the system of equations: 

$$\begin{array}{c}x+y+z=a\\ x^2+y^2+z^2=b^2\\ x·y=z^2\end{array}$$

where $a$ and $b$ are constants. Give the conditions that $a$ and $b$ must satisfy so that $x, y, z$ (the solutions of the system) are distinct positive numbers.