Решите уравнение: |x^2+4x-1|=4.

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

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

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

\[D = 4^{2} - 4 \cdot ( - 5) = 16 + 20 =\]

\[= 36\]

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

\[= 1\]

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

\[= \frac{- 10}{2} = - 5\]

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

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

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

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

\[= - 1\]

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

\[= - 3\]

\[Ответ:1;\ - 5;\ - 1;\ - 3.\]