Решите уравнение: |x^2+5x-3|=3.

Ответ:

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

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

\[D = 5^{2} - 4 \cdot 1 \cdot ( - 6) =\]

\[= 25 + 24 = 49\]

\[x_{1} = \frac{- 5 + \sqrt{49}}{2 \cdot 1} = \frac{- 5 + 7}{2} =\]

\[= \frac{2}{2} = 1\]

\[x_{2} = \frac{- 5 - \sqrt{49}}{2 \cdot 1} = \frac{- 5 - 7}{2} =\]

\[= - \frac{12}{2} = - 6\]

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

\[x(x + 5) = 0\]

\[x = 0,\ \ x + 5 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 5\]

\[Ответ:x = 1;\ x = - 6;x = 0;\ \]

\[x = - 5.\]