Решите уравнение: x^4-6x^2-7=0.

\[x^{4} - 6x^{2} - 7 = 0\]

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

\[t^{2} - 6t - 7 = 0\]

\[D = ( - 6)^{2} - 4 \cdot 1 \cdot ( - 7) =\]

\[= 36 + 28 = 64\]

\[t_{1} = \frac{6 + \sqrt{64}}{2} = \frac{6 + 8}{2} = \frac{14}{2} = 7\]

\[t_{2} = \frac{6 - \sqrt{64}}{2} = \frac{6 - 8}{2} = \frac{- 2}{2} =\]

\[= - 1\ \ (не\ подходит)\]

\[x^{2} = 7\]

\[x = \pm \sqrt{7}\]

\[Ответ:\sqrt{7}\ ;\ - \sqrt{7}.\]