Решите уравнение: x^3/|x|+3x+2=0.

Ответ:

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

\[x > 0\]

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

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

\[D = b^{2} - 4ac = 9 - 4 \cdot 1 \cdot 2 =\]

\[= 9 - 8 = 1\]

\[x_{1} = \frac{- 3 + 1}{2} = - \frac{2}{2} = - 1 \Longrightarrow\]

\[\Longrightarrow не\ подходит,\ x > 0\]

\[x_{2} = \frac{- 3 - 1}{2} = - \frac{4}{2} = - 2 \Longrightarrow\]

\[\Longrightarrow не\ подходит,\ x > 0\]

\[нет\ корней.\]

\[x < 0\]

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

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

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

\[= 9 - 4 \cdot ( - 1) \cdot 2 = 9 + 8 =\]

\[= 17\]

\[x_{1} = \frac{- 3 - \sqrt{11}}{- 2} = 1,5 + \frac{\sqrt{17}}{2} \Longrightarrow\]

\[\Longrightarrow не\ подходит,\ x < 0\]

\[x_{2} = \frac{- 3 + \sqrt{11}}{- 2} = 1,5 - \frac{\sqrt{17}}{2}\]

\[Ответ:x = 1,5 - \frac{\sqrt{17}}{2}.\]