Решите уравнение: (x^2-x)^2-5(x^2-x)-6=0.

\[\left( x^{2} - x \right)^{2} - 5\left( x^{2} - x \right) - 6 = 0\]

\[x^{2} - x = y:\]

\[y^{2} - 5y - 6 = 0\]

\[y_{1} + y_{2} = 5;\ \ y_{1} \cdot y_{2} = - 6\]

\[y_{1} = 6;\ \ y_{2} = - 1;\]

\[1)\ x^{2} - x = 6\]

\[x^{2} - x - 6 = 0\]

\[x_{1} + x_{2} = 1;\ \ x_{1} \cdot x_{2} = - 6\]

\[x_{1} = 3;\ \ x_{2} = - 2.\]

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

\[x^{2} - x + 1 = 0\]

\[D = 1 - 4 = - 3 < 0\]

\[нет\ корней.\]

\[Ответ:x = - 2;\ \ x = 3.\]