JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 25

Let $A=\begin{bmatrix}1&-1\\2&\alpha\end{bmatrix}$ and $B=\begin{bmatrix}\beta&1\\1&0\end{bmatrix}$, $\alpha,\beta\in\mathbf R$. Let $\alpha_1$ be the value of $\alpha$ which satisfies $(A+B)^2=A^2+\begin{bmatrix}2&2\\2&2\end{bmatrix}$ and $\alpha_2$ be the value of $\alpha$ which satisfies $(A+B)^2=B^2$. Then $|\alpha_1-\alpha_2|$ is equal to ______.