Решите уравнение: x^2-2|x|-8=0.

Ответ:

\[x² - 2|x| - 8 = 0\]

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

\[= 4 + 32 = 36\]

\[x_{1} = \frac{2 + \sqrt{36}}{2} = \frac{2 + 6}{2} = \frac{8}{2} = 4\]

\[x_{2} = \frac{2 - \sqrt{36}}{2} = \frac{2 - 6}{2} = - \frac{4}{2} =\]

\[= - 2\ (не\ подходит)\]

\[x^{2} + 2x - 8 = 0\]

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

\[= 4 + 32 = 36\]

\[x_{1} = \frac{- 2 + \sqrt{36}}{2} = \frac{- 2 + 6}{2} =\]

\[= \frac{4}{2} = 2\ (не\ подходит)\]

\[x_{2} = \frac{- 2 - \sqrt{36}}{2} = \frac{- 2 - 6}{2} =\]

\[= - \frac{8}{2} = - 4\]

\[Ответ:\ - 4;4.\]