Решите уравнение: x^4-8x^2-9=0.

\[x^{4} - 8x^{2} - 9 = 0\]

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

\[t^{2} - 8t - 9 = 0\]

\[D = ( - 8)^{2} - 4 \cdot 1 \cdot ( - 9) =\]

\[= 64 + 36 = 100\]

\[t_{1} = \frac{8 + \sqrt{100}}{2} = \frac{8 + 10}{2} = \frac{18}{2} =\]

\[= 9\]

\[t_{2} = \frac{8 - \sqrt{100}}{2} = \frac{8 - 10}{2} =\]

\[= \frac{- 2}{2} = - 1\ (не\ подходит)\]

\[x^{2} = 9\]

\[x = \pm 3\]

\[Ответ:3;\ - 3.\]