Решите уравнение: |x^2-4x-1|=4.

\[\left| x^{2} - 4x - 1 \right| = 4\]

\[x^{2} - 4x - 1 = 4\]

\[x^{2} - 4x - 5 = 0\]

\[D = ( - 4)^{2} - 4 \cdot 1 \cdot ( - 5) =\]

\[= 16 + 20 = 36\]

\[x_{1} = \frac{4 + \sqrt{36}}{2} = \frac{4 + 6}{2} = \frac{10}{2} = 5\]

\[x_{2} = \frac{4 - \sqrt{36}}{2} = \frac{4 - 6}{2} = \frac{- 2}{2} =\]

\[= - 1\]

\[x^{2} - 4x - 1 = - 4\]

\[x^{2} - 4x + 3 = 0\]

\[D = ( - 4)^{2} - 4 \cdot 3 = 16 - 12 = 4\]

\[x_{1} = \frac{4 + \sqrt{4}}{2} = \frac{4 + 2}{2} = \frac{6}{2} = 3\]

\[x_{2} = \frac{4 - \sqrt{4}}{2} = \frac{4 - 2}{2} = \frac{2}{2} = 1\]

\[Ответ:5;\ - 1;3;1.\]