026.2. б) \(\frac{2x+1}{3} - \frac{4x - x^2}{12} = \frac{x^2 - 4}{9}\)

Умножим обе части на 36: \[12(2x + 1) - 3(4x - x^2) = 4(x^2 - 4)\] \[24x + 12 - 12x + 3x^2 = 4x^2 - 16\] \[x^2 - 12x - 28 = 0\] \[D = (-12)^2 - 4 \cdot 1 \cdot (-28) = 144 + 112 = 256\] \[x_1 = \frac{12 + \sqrt{256}}{2} = \frac{12 + 16}{2} = 14\] \[x_2 = \frac{12 - \sqrt{256}}{2} = \frac{12 - 16}{2} = -2\] Ответ: \(x_1 = 14\), \(x_2 = -2\)