Question 185
For every pair of real numbers $a \ne b$ solve the system:
$$
\begin{cases}
3x+z = 2y+(a+b), \\
3x^2 + 3xz = y^2 + 2(a+b)y + ab, \\
x^3 + 3x^2z = y^2(a+b) + 2yab.
\end{cases}
$$
(Rublyov Bogdan)
$$
\begin{cases}
3x+z = 2y+(a+b), \\
3x^2 + 3xz = y^2 + 2(a+b)y + ab, \\
x^3 + 3x^2z = y^2(a+b) + 2yab.
\end{cases}
$$
(Rublyov Bogdan)