Решите уравнение: |x-2|=x^2.

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

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

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

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

\[= - 7 < 0 \Longrightarrow \ \ нет\ решения.\]

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

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

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

\[= 9\]

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

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

\[= - 2\]

\[Ответ:1;\ - 2.\]