7.2. For what values of $m$ do the equations $m x-1000=1021$ and $1021 x=m-1000 x$ have a common root?
Answer. For $m= \pm 2021$.

Solution. The roots of the given equation are the numbers $\frac{2021}{m}$ and $\frac{m}{2021}$, respectively. $\frac{2021}{m}=$ $\frac{m}{2021} \Leftrightarrow m^{2}=2021^{2} \Leftrightarrow m= \pm 2021$