If $lpha$ and $eta$ be the coefficients of

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. (1) $\alpha+\beta=60$

  2. (2) $\alpha+\beta=-30$

  3. (3) $\alpha-\beta=60$

  4. (4) $\alpha-\beta=-132$


Correct Option: , 4

Solution:

Using Binomial expansion

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