Решите уравнение: (x^2-4)/3-(5x-2)/6=1.

Ответ:

\[\frac{x^{2} - 4}{3} - \frac{5x - 2}{6} = 1\ \ | \cdot 6\]

\[2\left( x^{2} - 4 \right) - 5x + 2 = 6\]

\[2x^{2} - 8 - 5x + 2 - 6 = 0\]

\[2x^{2} - 5x - 12 = 0\]

\[D = 25 + 96 = 121\]

\[x_{1} = \frac{5 + 11}{4} = \frac{16}{4} = 4;\]

\[x_{2} = \frac{5 - 11}{4} = - \frac{6}{4} = - 1,5.\]

\[Ответ:x = - 1,5;x = 4.\]