Решить уравнение: (x^2-2)/3-(3x-1)/6=1.

Ответ:

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

\[2 \cdot \left( x^{2} - 2 \right) - (3x - 1) = 6\]

\[2x^{2} - 4 - 3x + 1 - 6 = 0\]

\[2x^{2} - 3x - 9 = 0\]

\[D = 9 + 72 = 81\]

\[x_{1} = \frac{3 + 9}{4} = 3;\]

\[x_{2} = \frac{3 - 9}{4} = - \frac{6}{4} = - 1,5.\]

\[Ответ:x = - 1,5;x = 3.\]