Matrices And Determinants

While solving a system of linear equations $A X=B$ using Cramer's rule with the usual notation if

$$ \Delta=\left|\begin{array}{ccc} 1 & 1 & 1 \\ 2 & -1 & 2 \\ -1 & 1 & 5 \end{array}\right|, \Delta_1=\left|\begin{array}{ccc} 5 & 1 & 1 \\ 4 & -1 & 2 \\ 11 & 1 & 5 \end{array}\right| \text { and } X=\left[\begin{array}{l} \alpha \\ 2 \\ \beta \end{array}\right] \text {, then } \alpha^2+\beta^2= $$