Question 2
$a$)Find integer solutions to $\left(3 x^{2} + y^{2} - 4 y - 17\right)^{3} - \left(2 x^{2} + 2 y^{2} - 4 y - 6\right)^{3} = \left(x^{2} - y^{2} - 11\right)^{3}$. $b$)If $5 x + 4 y + 3 z + 6 t = 20$ and $x \ge y \ge z \ge t \ge 0$, find the extrema of $x + y + z + t$.