What is the nicest way to prevent the "floor brackets" from touching in this example?
\alpha=
\begin{cases}
\left\lfloor \frac{(a_1+b_1)^2}{4} \right\rfloor & x \\
\left\lfloor \frac{(a_2+b_2)^2}{4} \right\rfloor & y \\
\end{cases}
This is a minimal example. The real example also has fractions where the numerator is a square of some subscripted terms.
I could use \bigl and \bigr but then the brackets look a bit short.

\begin{document} [\alpha= \begin{cases} \left\lfloor \frac{(a_1+b_1)^2}{4} \right\rfloor & x \[.7em]%%%%%<----it is a good measure. \left\lfloor \frac{(a_2+b_2)^2}{4} \right\rfloor & y \end{cases}] \end{document}`
– Sebastiano Aug 01 '20 at 11:40