A number $\alpha$ is said to satisfy the Diophantine condition with exponent $\beta$ iff for some constant $C>0$ the estimate $$ \left| \alpha - \frac{p}{q} \right| > \frac{C}{q^{2+\beta}} $$ holds for every rational fraction $p/q \in \mathbb{Q}$.

A question:

- Is it true that if $\alpha$ satisfies the Diophantine condition with exponent $\beta$ then the number $1/\alpha$ also satisfies the Diophantine condition with some exponent.