  For real $\xi$ we consider the irrationality measure function $\psi_\xi(t) =
\min_{1\leqslant q \leqslant t, q\in\mathbb{Z}} || q\xi ||$, where $||\cdot||$
- distance to the nearest integer. We prove that in the case
$\alpha\pm\beta\notin\mathbb{Z}$ there exist arbitrary large values of $t$ with
$$\Bigl | \frac{1}{\psi_\alpha(t)} - \frac{1}{\psi_\beta(t)} \Bigl | \geqslant
\sqrt5\left(1-\sqrt{\frac{\sqrt5-1}{2}}\right)t.$$ The constant on the
right-hand side is optimal.
