GR-HMS 2018 Problem 1

Let $(x_n), n\in\mathbb{N}$ be a sequence such that $x_{n+1}=3x_n^3+x_n, \forall n\in\mathbb{N}$ and $x_1=\frac{a}{b}$ where $a,b$ are positive integers such that $3\not|b$ . If $x_m$ is a square of a rational number for some positive integer $m$ , prove that $x_1$ is also a square of a rational number.