If α and β , be the coefficients of x 4 and x 2 , respectively in the expansion of x + x 2 - 1 6 +…

${\left(x+\sqrt{x^2-1}\right)}^6+{\left(x-\sqrt{x^2-1}\right)}^6=2\left[C_0{x}^6+C_2{x}^4\left(x^2-1\right)+C_4{x}^2{\left(x^2-1\right)}^2+C_6{\left(x^2-1\right)}^3\right]$

$=2\left[x^6+15\left(x^6-x^4\right)+15x^2\left(x^4-2x^2+1\right)+\left(-1+3x^2-3x^4+x^6\right)\right]$

$=2\left(32x^6-48x^4+18x^2-1\right)$

Now given that $\alpha \& \beta$ are the coefficients of $x^4 \& x^2$ respectively, hence

$\alpha =-96$ and $\beta =36$

$\therefore \mathrm{}\alpha -\beta =-132$