Let \( A=\left[\begin{array}{cc}1 & -1 \\ 2 & \alpha\end{array}\right] \) and \( B=\left[\begin{...

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