Решите уравнение: x^2-|x|-2=0.

Ответ:

\[x² - |x| - 2 = 0\]

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

\[= 1 + 8 = 9\]

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

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

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

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

\[= 1 + 8 = 9\]

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

\[= \frac{2}{2} = 1\ (не\ подходит)\]

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

\[= - \frac{4}{2} = - 2\]

\[Ответ:x = 2;\ x = - 2.\]