Решите уравнение: x^2-8|x|=0.

Ответ:

\[x² - 8|x| = 0\]

\[x \geq 0:\]

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

\[x(x - 8) = 0\]

\[x = 0,\ \ x - 8 = 0\]

\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }x = 8\]

\[x < 0:\]

\[x^{2} - 8 \cdot ( - x) = 0\]

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

\[x(x + 8) = 0\]

\[x = 0,\ \ x + 8 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 8\]

\[Ответ:x = 0;x = \pm 8.\]