Question: If $\alpha$ and $\beta$ be the coefficients 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:
(1) $\alpha+\beta=60$
(2) $\alpha+\beta=-30$
(3) $\alpha-\beta=60$
(4) $\alpha-\beta=-132$
Correct Option: , 4
Solution:
Using Binomial expansion
