Решите уравнение x^3-5x^2-x+5=0.

Ответ:

\[x^{3} - 5x^{2} - x + 5 = 0\]

\[x^{2}(x - 5) - (x - 5) = 0\]

\[(x - 5)\left( x^{2} - 1 \right) = 0\]

\[(x - 5)(x - 1)(x + 1) = 0\]

\[x - 5 = 0;\ \ \ x - 1 = 0;\ \ \ x + 1 = 0\]

\[x = 5\ \ \ \ \ \ \ \ \ \ \ \ \ x = 1\ \ \ \ \ \ \ \ \ \ \ \ x = - 1\]

\[Ответ:x = \pm 1;\ \ x = 5.\]