\[9x^{4} - 19x^{2} + 2 = 0\]
\[Пусть\ \ t = x^{2} \geq 0:\]
\[9t^{2} - 19t + 2 = 0\]
\[D = 361 - 72 = 289 = 17^{2}\]
\[t_{1} = \frac{19 + 17}{18} = 2;\ \ \]
\[t_{2} = \frac{19 - 17}{18} = \frac{2}{18} = \frac{1}{9}.\]
\[Подставим:\ \]
\[x^{2} = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^{2} = \frac{1}{9}\]
\[x = \pm \sqrt{2}\ \ \ \ \ \ \ \ \ \ \ \ x = \pm \frac{1}{3}\]
\[Ответ:\ x = \pm \sqrt{2};\ x = \pm \frac{1}{3}.\]