Решите уравнение: (3x+1)/4-(7x-x^2)/10=(x^2-1)/8.

Ответ:

\[\frac{3x + 1}{4} - \frac{7x - x^{2}}{10} = \frac{x^{2} - 1}{8}\ \ \ \ \ \ | \cdot 40\ \]

\[10 \cdot (3x + 1) - 4 \cdot \left( 7x - x^{2} \right) =\]

\[= 5 \cdot (x² - 1)\]

\[30x + 10 - 28x + 4x^{2} - 5x^{2} + 5 = 0\]

\[- x^{2} + 2x + 15 = 0\]

\[x^{2} - 2x - 15 = 0\]

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

\[x_{1} \cdot x_{2} = - 15 \Longrightarrow x_{1} = - 3\ \ \ и\ \ \]

\[\ x_{2} = 5\]

\[Ответ:x = - 3\ \ и\ \ x = 5.\]