Решите уравнение: x^3+3x^2+x-2=0.

\[x³ + 3x² + x - 2 = 0\]

\[P( - 2) =\]

\[= ( - 2)^{3} + 3 \bullet ( - 2)^{2} + ( - 2) - 2 =\]

\[= - 8 + 12 - 2 - 2 = 0.\]

\[(x + 2)\left( x^{2} + x - 1 \right) = 0\]

\[x + 2 = 0\]

\[x = - 2.\]

\[x^{2} + x - 1 = 0\]

\[D = 1^{2} - 4 \bullet 1 \bullet ( - 1) = 1 + 4 =\]

\[= 5\]

\[x_{1} = \frac{- 1 + \sqrt{5}}{2};\ \ \ \ x_{2} = \frac{- 1 - \sqrt{5}}{2}\]

\[Ответ:\ - 2;\ \ \frac{- 1 + \sqrt{5}}{2};\ \]

\[\ \frac{- 1 - \sqrt{5}}{2}.\]