If \( \{(\alpha+1)(\beta-1)+(\beta+1)(\alpha-1)\} a+(\alpha-1)(\beta-1)=0 \) and \( a(\alpha+1)(...

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If \( \{(\alpha+1)(\beta-1)+(\beta+1)(\alpha-1)\} a+(\alpha-1)(\beta-1)=0 \) and \( a(\alpha+1)(\beta+1)-(\alpha-1)(\beta-1)=0 \)
Also, let \( A=\left\{\frac{\alpha+1}{\alpha-1}, \frac{\beta+1}{\beta-1}\right\} \) and \( B=\left\{\frac{2 \alpha}{\alpha+1}, \frac{2 \beta}{\beta+1}\right\} \). If \( A \cap B \neq \phi \), then find all the permissible values of the parameter ' \( a \) '.
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