Решите уравнение: ||x^2+6x+5|-1|=3.

\[\left| \left| x^{2} + 6x + 5 \right| - 1 \right| = 3\]

\[\left| x^{2} + 6x + 5 \right| - 1 = 3\]

\[\left| x^{2} + 6x + 5 \right| = 4\]

\[x^{2} + 6x + 5 = 4\]

\[x^{2} + 6x + 1 = 0\]

\[D = 6^{2} - 4 \cdot 1 \cdot 1 = 36 - 4 = 32\]

\[x_{1} = \frac{- 6 + \sqrt{32}}{2} = \frac{- 6 + 4\sqrt{2}}{2} =\]

\[= - 3 + 2\sqrt{2}\]

\[x_{2} = \frac{- 6 - \sqrt{32}}{2} = \frac{- 6 - 4\sqrt{2}}{2} =\]

\[= - 3 - 2\sqrt{2}\]

\[x^{2} + 6x + 5 = - 4\]

\[x^{2} + 6x + 9 = 0\]

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

\[x + 3 = 0\]

\[x = - 3.\]

\[\left| x^{2} + 6x + 5 \right| - 1 = - 3\]

\[\left| x^{2} + 6x + 5 \right| = - 2 \Longrightarrow \ \]

\[\Longrightarrow \ \ нет\ решения.\]

\[Ответ:\ - 3 + 2\sqrt{2};\ \ - 3 - 2\sqrt{2};\ \]

\[\ - 3.\]