If \( \alpha \) and \( \beta \) be the coefficient of \( x^{4} \) and \( x^{2} \) respectively i...

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If \( \alpha \) and \( \beta \) be the coefficient of \( x^{4} \) and \( x^{2} \) respectively in the expansion of \( \left(x+\sqrt{x^{2}-1}\right)^{6}+\left(x-\sqrt{x^{2}-1}\right)^{6} \), then :
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