Найдите координаты точек пересечения графиков функций y=x^3/(x+20) и y=x^2-20.

\[y = \frac{x^{3}}{x + 20};\ \ \ y = x^{2} - 20\]

\[\frac{x^{3}}{x + 20} = x^{2} - 20^{\backslash x + 20}\ \ \ \ \ \ \ \ x \neq - 20\]

\[x^{3} = x^{3} - 20x + 20x^{2} - 400\]

\[x^{3} - x^{3} + 20x^{2} - 20x - 400 = 0\]

\[20x^{2} - 20x - 400 = 0\ \ \ \ \ \ \ |\ :20\]

\[x^{2} - x - 20 = 0\]

\[x_{1} + x_{2} = 1;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x_{1} \cdot x_{2} = - 20\]

\[x_{1} = 5;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x_{2} = - 4.\]

\[y_{1} = 25 - 20 = 5;\ \ \ \ y_{2} = 16 - 20 = - 4.\]

\[Ответ:графики\ пересекаются\ в\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ точках\ (5;5)\ и\ ( - 4; - 4).\]