Найдите корни уравнения: (x^2-11)/7=(x-x^2)/2.

Ответ:

\[\frac{x^{2} - 11}{7} = \frac{x - x^{2}}{2}\ \ \ \ \ | \cdot 14\]

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

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

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

\[9x² - 7x - 22 = 0\]

\[D = b^{2} - 4ac =\]

\[= 49 - 4 \cdot 9 \cdot ( - 22) =\]

\[= 49 + 792 = 841\]

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

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

\[= - 1\frac{2}{9}\]

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