Решите уравнение: x^10-31x^5-32=0.

Ответ:

\[x^{10} - 31x^{5} - 32 = 0\]

\[Пусть\ a = x^{5}:\]

\[a^{2} - 31a - 32 = 0\]

\[a_{1} + a_{2} = 31;\ \ \ a_{1} \cdot a_{2} = - 32\]

\[a_{1} = 32;\ \ \ \ a_{2} = - 1.\]

\[a = 32:\]

\[x^{5} = 32\]

\[x = 2.\]

\[a = - 1:\]

\[x^{5} = - 1\]

\[x = - 1.\]

\[Ответ:\ - 2;1.\]