Решите уравнение: x^6-7x^3-8=0.

Ответ:

\[x^{6} - 7x^{3} - 8 = 0\]

\[Пусть\ x^{3} = y:\]

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

\[y_{1} + y_{2} = 7;\ \ \ y_{1} \cdot y_{2} = - 8\]

\[y_{1} = 8;\ \ \ y_{2} = - 1.\]

\[1)\ x^{3} = 8\]

\[x = 2.\]

\[2)\ x^{3} = - 1\]

\[x = - 1.\]

\[Ответ:x = - 1;x = 2.\]