$a)$

$\left|x^2-4\right|=1$

$x^2-4=1\vee x^2-4=-1$

$x^2=5\vee x^2=3$

$x=\sqrt{5}\vee x=-\sqrt{5}\vee x=\sqrt{3}\vee x=-\sqrt{3}$

$\underline{\underline{x\in \left\{-\sqrt{5},-\sqrt{3},\sqrt{3},\sqrt{5}\right\}}}$