Решите уравнение: (2x+1)/3-(4x-x^2)/12=(x^2-4)/9.

Ответ:

\[12 \cdot (2x + 1) - 3 \cdot \left( 4x - x^{2} \right) =\]

\[= 4 \cdot \left( x^{2} - 4 \right)\]

\[24x + 12 - 12x + 3x^{2} - 4x^{2} + 16 = 0\]

\[- x² + 12x + 28 = 0\ \ \ \ \ \ \ \ | \cdot ( - 1)\]

\[x^{2} - 12x - 28 = 0\]

\[x_{1} + x_{2} = 12\]

\[x_{1} \cdot x_{2} = - 28 \Longrightarrow x_{1} = 14;\ \ \]

\[x_{2} = - 2\]

\[Ответ:\ \ x = 14\ \ \ \ и\ \ \ x = - 2.\]