\[x^{4} - 18x^{2} + 32 = 0\]
\[Пусть\ x^{2} = a \geq 0:\]
\[a^{2} - 18a + 32 = 0\]
\[D = 81 - 32 = 49\]
\[a_{1} = 9 + 7 = 16;\ \ \ \]
\[a_{2} = 9 - 7 = 2.\]
\[Подставим:\]
\[1)\ x^{2} = 16\]
\[x = \pm 4.\]
\[2)\ x^{2} = 2\]
\[x = \pm \sqrt{2}.\]
\[Ответ:x = \pm 4;\ \ x = \pm \sqrt{2}.\]