Sum of the positive roots of the equation $$ \left|\begin{array}{ccc} x^2+2 x & x+2 & 1 \\ 2 x+1 & x-1 & 1 \\ x+2 & -1 & 1 \end{array}\right|=0 \text { is } $$

If the solution of the system of simultaneous linear equations $x+y-z=6,3 x+2 y-z=5$ and $2 x-y-2 z+3=0$ is $x=\alpha, y=\beta, z=y$, then $\alpha+\beta=$

$$ \left|\begin{array}{ccc} 1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3 \end{array}\right|= $$

If $A=\left[\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right]$ and $\alpha A^2+\beta A=2 I$ for some $\alpha, \beta \in R$, then $\alpha+\beta=$