Решите уравнение: (x(2-x))/2+(3(x-3)^2)/2=2 1/2-(2(4-x)^2)/3.

Ответ:

\[\frac{x(2 - x)}{2} + \frac{3 \cdot (x - 3)^{2}}{2} =\]

\[= 2\frac{1}{2} - \frac{2 \cdot (4 - x)^{2}}{3}\ \ \ \ \ \ \ | \cdot 6\]

\[3x(2 - x) + 9\left( x^{2} - 6x + 9 \right) =\]

\[= 15 - 4\left( 16 - 8x + x^{2} \right)\]

\[10x^{2} - 80x + 130 = 0\ \ \ \ \ |\ :10\]

\[x^{2} - 8x + 13 = 0\]

\[D = 16 - 13 = 3\]

\[x_{1} = 4 + \sqrt{3};\ \ \ x_{2} = 4 - \sqrt{3}.\]