Решите уравнение: x^3-7x+6=0.

Ответ:

\[x^{3} - 7x + 6 = 0\]

\[x^{3} - x - 6x + 6 = 0\]

\[x(x² - 1) - 6(x - 1) = 0\]

\[x(x - 1)(x + 1) - 6(x - 1) = 0\]

\[(x - 1)\left( x(x + 1) - 6 \right) = 0\]

\[(x - 1)\left( x^{2} + x - 6 \right) = 0\]

\[x = 1;\]

\[x^{2} + x - 6 = 0\]

\[x_{1} + x_{2} = - 1;\ \ \ x_{1} \cdot x_{2} = - 6\]

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

\[Ответ:x = - 3;\ \ x = 1;\ \ x = 2.\]