Решите уравнение: (x^2+16x)(корень из (x)-2)(x^2-2x-24)=0.

Ответ:

\[x(x + 16) = 0\]

\[x = 0,\ \ x + 16 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 16.\]

\[\sqrt{x} = 2\ \ \]

\[x = 4.\]

\[D = ( - 2)^{2} - 4 \cdot 1 \cdot ( - 24) =\]

\[= 4 + 96 = 100\]

\[x_{1} = \frac{2 + \sqrt{100}}{2} = \frac{2 + 10}{2} =\]

\[= \frac{12}{2} = 6;\]

\[x_{2} = \frac{2 - \sqrt{100}}{2} = \frac{2 - 10}{2} =\]

\[= - \frac{8}{2} = - 4.\]

\[Ответ:x = 0;\ \ x = 6;\ \ x = \pm 4;\ \]

\[x = - 16.\]