Solution
= Solution
The <Liouville approximation theorem> says that for a real <algebraic number> $\xi$ of degree $d\geq2$, there is a constant $C(\xi)>0$ such that
$$
\boxed{\left|\xi-\frac pq\right|\geq\frac{C(\xi)}{q^d}}
$$
for all integers $p$ and $q\geq1$ with $p/q\ne\xi$. In particular a <quadratic irrational> cannot have arbitrarily accurate rational approximations of order $o(q^{-2})$.