Решите уравнение: (2x-7)^2-7*(7-2x)=0.

Ответ:

\[(2x - 7)^{2} - 7 \cdot (7 - 2x) = 0\]

\[(7 - 2x)^{2} - 7 \cdot (7 - 2x) = 0\]

\[(7 - 2x)(7 - 2x - 7) = 0\]

\[(7 - 2x) \cdot ( - 2x) = 0\]

\[- 2x \cdot (7 - 2x) = 0\]

\[x = 0,\ \ 7 - 2x = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x = 7\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 3,5.\]

\[Ответ:x = 0;x = 3,5.\]