Решите уравнение: |x+2|=x^2.

\[|x + 2| = x^{2}\]

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

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

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

\[= 1 + 8 = 9\]

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

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

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

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

\[D = 1^{2} - 4 \cdot 1 \cdot 2 = 1 - 8 =\]

\[= - 7 < 0 - нет\ решения.\]

\[Ответ:2;\ - 1.\]