Решите уравнение x^4+7x^2-8=0.

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

\[Сделаем\ замену:\ \ \ t = x^{2}\]

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

\[D = 49 + 32 = 81\]

\[t_{1} = \frac{- 7 + 9}{2} = \frac{2}{2} = 1;\ \ \ \ \ \ \ \]

\[t_{2} = \frac{- 7 - 9}{2} = - \frac{16}{2} = - 8.\]

\[Подставим:\]

\[1)\ x^{2} = 1\]

\[x = \pm 1.\]

\[2)\ x^{2} = - 8\]

\[нет\ корней.\]

\[Ответ:x = \pm 1.\]