Explanation

(b)
Here, $\alpha + \ \beta + \gamma = - 2$ ...(i)
$\alpha\ \beta + \beta\gamma + \gamma\alpha = - 3$ ...(ii)
and $\alpha\beta\gamma = 1$ ...(iii)
On solving Eq. (ii), we get
$\alpha^{2}\beta^{2} + \beta^{2}\gamma^{2} + \gamma^{2}\alpha^{2} + 2\alpha\beta\gamma(\alpha + \beta + \gamma) = 9$
$\Rightarrow \ \alpha^{2}\beta^{2} + \beta^{2}\gamma^{2} + \gamma^{2}\alpha^{2} = 9 - 2(1)( - 2) = 13$
Now, $\alpha^{- 2} + \beta^{- 2} + r^{- 2} = \frac{\beta^{2}\gamma^{2} + \gamma^{2}\alpha^{2} + \alpha^{2}\beta^{2}}{(\alpha\beta\gamma)^{2}} = \frac{13}{1} = 13$