Решите уравнение: x^2-7|x|+12=0.

\[x^{2} - 7|x| + 12 = 0\]

\[1)\ x > 0:\]

\[x^{2} - 7x + 12 = 0\]

\[x_{1} + x_{2} = 7;\ \ \ x_{1} \cdot x_{2} = 12\]

\[x_{1} = 3;\ \ x_{2} = 4.\]

\[2)\ x < 0:\]

\[x^{2} + 7x + 12 = 0\]

\[x_{1} + x_{2} = - 7;\ \ \ x_{1} \cdot x_{2} = 12\]

\[x_{1} = - 4;\ \ x_{2} = - 3.\ \]

\[Ответ:x = \pm 3;\ \ x = \pm 4.\]