Решите уравнение: 5x^4+3x^2-2=0.

\[5x^{4} + 3x² - 2 = 0\ \]

\[Пусть\ \ t = x^{2} \geq 0:\]

\[5t^{2} + 3t - 2 = 0\]

\[D = 9 + 40 = 49\]

\[t_{1} = \frac{- 3 + 7}{10} = \frac{4}{10} = \frac{2}{5};\ \ \]

\[t_{2} = \frac{- 3 - 7}{10} =\]

\[= - 1 < 0\ (не\ подходит).\]

\[Подставим:\]

\[\ x^{2} = \frac{2}{5}\]

\[x = \pm \sqrt{\frac{2}{5}}\]

\[Ответ:\ x = \pm \sqrt{\frac{2}{5}}.\]