$$\left(\frac{\sqrt{5} + \sqrt{7}}{\sqrt{5} - \sqrt{7}} + \frac{\sqrt{5} - \sqrt{7}}{\sqrt{5} + \sqrt{7}}\right)^2$$ =

$$\left(\frac{\sqrt{5} + \sqrt{7}}{\sqrt{5} - \sqrt{7}} + \frac{\sqrt{5} - \sqrt{7}}{\sqrt{5} + \sqrt{7}}\right)^2$$ = {$$\frac{\left(\left(\sqrt{\ 5}+\sqrt{\ 7}\right)^2-\ \left(\sqrt{\ 5}-\sqrt{\ 7}\right)^2\right)}{\left(\sqrt{\ 5}^{ }+\sqrt{\ }7\right)\left(\sqrt{\ 5}^{ }-\sqrt{\ }7\right)}$$}^2

= $$\left(\frac{\left(\left(5\ +7\ +2.\sqrt{\ 5}.\sqrt{\ 7}\right)+\left(5\ +7\ -2.\sqrt{\ 5}.\sqrt{\ 7}\right)\right)}{5-7}\right)^2$$ = $$\left(\frac{\left(12+12\right)}{-2}\right)^2=\ \left(-12\right)^2\ =144\ Answer$$