# Ultimate Resemblance

Geometry Level 4

$\large{\begin{cases} {x \sqrt{1-y^2} = a^2} \\ { y \sqrt{1-x^2} =a } \end{cases} }$

If the system of equations above have a real solution if and only if $$a \in [\alpha , \beta ]$$, then find the value of $$\alpha + \beta$$.

×