Let A= [1, -1; 2, α] and B= [β, 1; 1, 0], α, β ∈ R. Let α_1 be the value of α which satisfies (A+B)^2=A^2+ [2, 2; 2, 2] and α_2 be the value of α…

Let $\displaystyle A=\left[\begin{array}{cc}1 & -1 \\ 2 & \alpha\end{array}\right]$ and $\displaystyle B=\left[\begin{array}{cc}\beta & 1 \\ 1 & 0\end{array}\right], \alpha, \beta \in \mathbf{R}$. Let $\displaystyle \alpha_1$ be the value of $\displaystyle \alpha$ which satisfies $\displaystyle (A+B)^2=A^2+\left[\begin{array}{ll}2 & 2 \\ 2 & 2\end{array}\right]$ and $\displaystyle \alpha_2$ be the value of $\displaystyle \alpha$ which satisfies $\displaystyle (A+B)^2=B^2$. Then $\displaystyle \left|\alpha_1-\alpha_2\right|$ is equal to \_\_\_\_.