Определите значения x, при которых верно равенство: (x^2-11)/7=(x-x^2)/2.

Ответ:

\[\frac{x^{2} - 11}{7} = \frac{x - x^{2}}{2}\]

\[2\left( x^{2} - 11 \right) = 7\left( x - x^{2} \right)\]

\[2x^{2} - 22 = 7x - 7x^{2}\]

\[9x^{2} - 7x - 22 = 0\]

\[D = 49 + 792 = 841 = 29^{2}\]

\[x_{1} = \frac{7 + 29}{18} = \frac{36}{18} = 2;\]

\[x_{2} = \frac{7 - 29}{18} = - \frac{22}{18} = - \frac{11}{9}.\]

\[Ответ:при\ x = - 1\frac{2}{9};x = 2.\]