Question 92
Let $n \ge 2$ be an integer and $r = \sqrt[3]{2}$. Prove that there do not exist rational numbers $a_0, a_1, \dots, a_{n-1}$, not all of them equal to zero, such that
$$
a_0 + a_1 r + a_2 r^2 + \dots + a_{n-1} r^{n-1} = 0.
$$
$$
a_0 + a_1 r + a_2 r^2 + \dots + a_{n-1} r^{n-1} = 0.
$$