Решите уравнение: |x^2-x-1|=1.

Ответ:

\[\left| x^{2} - x - 1 \right| = 1\]

\[x² - x - 2 = 0\]

\[D = ( - 1)^{2} - 4 \cdot 1 \cdot ( - 2) =\]

\[= 1 + 8 = 9\]

\[x_{1} = \frac{1 + \sqrt{9}}{2} = \frac{1 + 3}{2} = \frac{4}{2} = 2\]

\[x_{2} = \frac{1 - \sqrt{9}}{2} = \frac{1 - 3}{2} = - \frac{2}{2} = - 1\]

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

\[x(x - 1) = 0\]

\[x = 0,\ \ x - 1 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 1\]

\[Ответ:2;\ - 1;0;1.\]