Question 1
(HUN) Solve the following system of equations:
$$\begin{cases}x+y+z=a,\\x^2+y^2+z^2=b^2,\\xy=z^2,\end{cases}$$
where $a$ and $b$ are given real numbers. What conditions must hold on $a$ and $b$ for the solutions to be positive and distinct?
$$\begin{cases}x+y+z=a,\\x^2+y^2+z^2=b^2,\\xy=z^2,\end{cases}$$
where $a$ and $b$ are given real numbers. What conditions must hold on $a$ and $b$ for the solutions to be positive and distinct?