Question 3
a) Find all integer solutions of
$$(3x^2+y^2-4y-17)^3-(2x^2+2y^2-4y-6)^3=(x^2-y^2-11)^3.$$
b) Given $5x+4y+3z+6t=20$ and real numbers $x\ge y\ge z\ge t\ge0$, find the maximum and minimum of $x+y+z+t$.
$$(3x^2+y^2-4y-17)^3-(2x^2+2y^2-4y-6)^3=(x^2-y^2-11)^3.$$
b) Given $5x+4y+3z+6t=20$ and real numbers $x\ge y\ge z\ge t\ge0$, find the maximum and minimum of $x+y+z+t$.