Решите уравнение: x^3/|x|+x+3=0.

Ответ:

\[\frac{x^{3}}{|x|} + x + 3 = 0\]

\[1)\ x > 0:\]

\[\frac{x^{3}}{x} + x + 3 = 0\]

\[x^{2} + x + 3 = 0\]

\[D = b^{2} - 4ac = 1 - 4 \cdot 1 \cdot 3 =\]

\[= 1 - 12 = - 11 < 0\]

\[нет\ решений.\]

\[2)\ x < 0:\]

\[\frac{x^{3}}{- x} + x + 3 = 0\]

\[- x^{2} + x + 3 = 0\]

\[x^{2} - x - 3 = 0\]

\[D = b^{2} - 4ac =\]

\[= 1 - 4 \cdot ( - 1) \cdot 3 =\]

\[= 1 + 12 = 13\]

\[x_{1} = \frac{1 - \sqrt{13}}{2};\ \]

\[x_{2} = \frac{1 + \sqrt{13}}{2} > 0 -\]

\[не\ подходит.\]

\[Ответ:x = \frac{1 - \sqrt{13}}{2}.\]