Решите уравнение: x^2-4|x|-32=0.

\[x² - 4|x| - 32 = 0\]

\[D = ( - 4)^{2} - 4 \cdot 1 \cdot ( - 32) =\]

\[= 16 + 128 = 144\]

\[x_{1} = \frac{4 + \sqrt{144}}{2} = \frac{4 + 12}{2} =\]

\[= \frac{16}{2} = 8\]

\[x_{2} = \frac{4 - \sqrt{144}}{2} = \frac{4 - 12}{2} =\]

\[= - \frac{8}{2} = - 4\ (не\ подходит).\]

\[D = 4^{2} - 4 \cdot 1 \cdot ( - 32) =\]

\[= 16 + 128 = 144\]

\[x_{1} = \frac{- 4 + \sqrt{144}}{2} = \frac{- 4 + 12}{2} =\]

\[= \frac{8}{2} = 4\ (не\ подходит).\]

\[x_{2} = \frac{- 4 - \sqrt{144}}{2} = \frac{- 4 - 12}{2} =\]

\[= - \frac{16}{2} = - 8\]

\[Ответ:x = 8;\ x = - 8.\]