Решите уравнение: x^4-7x^2-8=0.

\[x^{4} - 7x^{2} - 8 = 0\]

\[t = x^{2};\ \ \ \ \ t \geq 0\]

\[t^{2} - 7t - 8 = 0\]

\[D = ( - 7)^{2} - 4 \cdot 1 \cdot ( - 8) =\]

\[= 49 + 32 = 81\]

\[t_{1} = \frac{7 + \sqrt{81}}{2} = \frac{7 + 9}{2} = \frac{16}{2} = 8\]

\[t_{2} = \frac{7 - \sqrt{81}}{2} = \frac{7 - 9}{2} = \frac{- 2}{2} =\]

\[= - 1\ не\ подходит\]

\[x^{2} = 8\]

\[x = \pm \sqrt{8} = \pm 2\sqrt{2}\]

\[Ответ:2\sqrt{2};\ - 2\sqrt{2}.\]