Решите уравнение: x^3-31x+30=0.

Ответ:

\[x^{3} - 31x + 30 = 0\]

\[x^{3} - x - 30x + 30 = 0\ \]

\[x\left( x^{2} - 1 \right) - 30(x - 1) = 0\]

\[x(x - 1)(x + 1) - 30(x - 1) = 0\]

\[(x - 1)\left( x^{2} + x - 30 \right) = 0\]

\[x - 1 = 0\]

\[x = 1.\]

\[x^{2} + x - 30 = 0\]

\[x_{1} + x_{2} = - 1;\ \ \ x_{1} \cdot x_{2} = - 30\]

\[x_{1} = - 6;\ \ x_{2} = 5.\]

\[Ответ:x = - 6;\ \ x = 1;\ \ x = 5.\]