Решите уравнение: x^8-82x^4+81=0.

\[x^{8} - 82x^{4} + 81 = 0\]

\[Пусть\ a = x^{4}:\]

\[a^{2} - 82a + 81 = 0\]

\[a_{1} + a_{2} = 82;\ \ \ \ a_{1} \cdot a_{2} = 81\]

\[a_{1} = 81;\ \ \ a_{2} = 1.\]

\[a = 81:\]

\[x^{4} = 81\]

\[x = \pm 3.\]

\[a = 1:\]

\[x^{4} = 1\]

\[x = \pm 1.\]

\[Ответ:\ \pm 1;\ \pm 3.\]