\[(x - 1)\sqrt{x^{2} - 4} = 0\]
\[x - 1 = 0;\ \ x = 1\]
\[\sqrt{x^{2} - 4} = 0;\]
\[\ x^{2} - 4 = 0\]
\[x^{2} = 4\]
\[\ x = \pm 2.\ \]