Решите уравнение: 3x^4+8x^2-3=0.

Ответ:

\[3x^{4} + 8x² - 3 = 0\]

\[Пусть\ t = x^{2} \geq 0:\ \ \]

\[3t^{2} + 8t - 3 = 0\]

\[t_{1} + t_{2} = - \frac{8}{3};\ \ t_{1} \cdot t_{2} = - 1\]

\[\Longrightarrow t_{1} = - 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t_{2} = \frac{1}{3}\]

\[x^{2} = - 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\ x}^{2} = \frac{1}{3}\]

\[нет\ решения;\ x = \pm \sqrt{\frac{1}{3}} = \pm \frac{1}{\sqrt{3}}\]

\[Ответ:\ \pm \frac{1}{\sqrt{3}}.\]