I see you've uploaded a math problem written in Vietnamese. Here’s a breakdown of the two tasks provided:

1. Solving the system of equations: x^3 + z^3 = 3y \\ y^3 + x^3 = 3z \\ z^3 + y^3 = 3x \end{cases}$$ The goal here is to find the values of $$x$$, $$y$$, and $$z$$ that satisfy this system.
2. Proving the equation has three solutions for two distinct integer values $a$ and $b$: $\left( \sqrt{x-1} \right) \left[ x^2 - 2(a+b)x + ab + 2 \right] = 0$ This is the second part of the problem where we need to show that the equation has exactly three solutions.

Would you like me to go through the full solutions step by step?