MathNet 1978 — Part 01 Question 13

Let $x_n = (1 + \sqrt{2} + \sqrt{3})^{n}$. We may write $x_n = a_n + b_n \sqrt{2} + c_n \sqrt{3} + d_n \sqrt{6}$, where $a_n, b_n, c_n, d_n$ are integers. Find the limit as $n$ tends to infinity of $b_n / a_n$, $c_n / a_n$, $d_n / a_n$.