Решите уравнение: x^5+5x^3-6x^2=0.

\[x^{5} + 5x^{3} - 6x^{2} = 0\]

\[x^{2}\left( x^{3} + 5x - 6 \right) = 0\]

\[x^{2}\left( x^{3} - x + x + 5x - 6 \right) = 0\]

\[1)\ x^{2} = 0\]

\[x = 0.\]

\[2)\ \left( x^{3} - x \right) + (6x - 6) = 0\]

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

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

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

\[x - 1 = 0\]

\[x = 1.\]

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

\[D = 1 - 24 = - 23 < 0\]

\[нет\ корней.\]

\[Ответ:x = 0;x = 1.\]