Question 3
a) Given real numbers $a,b$ satisfying $a^3+b^3+6ab=8$, find all possible values of $a+b$.
b) Find all real $a$ such that both $a+3\sqrt{11}$ and $\dfrac1a-3\sqrt{11}$ are integers.
b) Find all real $a$ such that both $a+3\sqrt{11}$ and $\dfrac1a-3\sqrt{11}$ are integers.