VMO 2020 Problem 1

Let a sequence $(x_n)$ satisfy : $x_1=1$ and $x_{n+1}=x_n+3\sqrt{x_n} + \frac{n}{\sqrt{x_n}}$ , $\forall$ n $\ge1$ a) Prove lim $\frac{n}{x_n}=0$ b) Find lim $\frac{n^2}{x_n}$