Решите уравнение: 25x^4-25x^2+6=0.

\[25x^{4} - 25x^{2} + 6 = 0\]

\[x^{2} = y \geq 0:\]

\[25y^{2} - 25y + 6 = 0\]

\[D = 625 - 600 = 25\]

\[y_{1} = \frac{25 + 5}{50} = \frac{30}{50} = \frac{3}{5};\ \]

\[y_{2} = \frac{25 - 5}{50} = \frac{20}{50} = \frac{2}{5};\]

\[1)\ x^{2} = \frac{3}{5}\]

\[x = \pm \sqrt{\frac{3}{5}} = \pm \frac{\sqrt{15}}{5}.\]

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

\[x = \pm \sqrt{\frac{2}{5}} = \pm \frac{\sqrt{10}}{5}.\]

\[Ответ:x = \pm \frac{\sqrt{15}}{5};\ \ x = \pm \frac{\sqrt{10}}{5}.\]