Question 3
Let $x$, $y$ and $z$ be positive integers such that
$$\begin{cases}z^3-x^3-y^3=3xyz,\\x^2+y^2+z^2\le150.\end{cases}$$
What is the maximum possible value of $x+y+z$?
$$\begin{cases}z^3-x^3-y^3=3xyz,\\x^2+y^2+z^2\le150.\end{cases}$$
What is the maximum possible value of $x+y+z$?