Не выполняя построения, найдите координаты точек пересечения графиков уравнений x² + y – 10 = 0 и y = 3x² – x – 4.

\[x^{2} + y - 10 = 0 \rightarrow y = 10 - x^{2}\]

\[y = 3x^{2} - x - 4\]

\[3x^{2} - x - 4 = 10 - x^{2}\]

\[3x^{2} + x^{2} - x - 4 - 10 = 0\]

\[4x^{2} - x - 14 = 0\]

\[D = 1 + 224 = 225\]

\[x_{1} = \frac{1 + 15}{8} = 2;\ \ \]

\[x_{2} = \frac{1 - 15}{8} = - \frac{14}{8} = - \frac{7}{4}.\]

\[y_{1} = 10 - 4 = 6;\]

\[y_{2} = 10 - \left( - \frac{7}{4} \right)^{2} = 10 - \frac{49}{16} =\]

\[= 10 - 3\frac{1}{16} = 9\frac{16}{16} - 3\frac{1}{16} = 6\frac{15}{16}.\]

\[Координаты\ точек\ пересечения\ \]

\[графиков:(2;6)\ \ и\ \left( - 1\frac{3}{4};6\frac{15}{16} \right).\]