Решите уравнение: x^2-4|x|+5x=0.

Ответ:

\[x² - 4|x| + 5x = 0\]

\[x \geq 0:\]

\[x^{2} - 4x + 5x = 0\]

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

\[x(x + 1) = 0\ \]

\[x = 0,\ \ x + 1 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 1\ (не\ подходит)\]

\[x < 0:\]

\[x^{2} - 4 \cdot ( - x) + 5x = 0\]

\[x^{2} + 4x + 5x = 0\]

\[x^{2} + 9x = 0\]

\[x(x + 9) = 0\]

\[x = 0,\ \ x + 9 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 9\]

\[Ответ:x = 0;\ x = - 9.\]