Question 137
Prove that for any rational numbers $a$ and $b$ the graph of the function
$$
f(x) = x^3 - 6abx - 2a^3 - 4b^3, \quad x \in \mathbb{R},
$$
has exactly one common point with the $x$-axis.
$$
f(x) = x^3 - 6abx - 2a^3 - 4b^3, \quad x \in \mathbb{R},
$$
has exactly one common point with the $x$-axis.