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

Ответ:

\[\frac{x^{2} + 1}{5} - \frac{x + 1}{4} = 1\ \ \ | \cdot 20\]

\[4\left( x^{2} + 1 \right) - 5(x + 1) = 20\]

\[4x^{2} + 4 - 5x - 5 - 20 = 0\]

\[4x^{2} - 5x - 21 = 0\]

\[D = 25 + 336 = 361 = 19^{2}\]

\[x_{1} = \frac{5 + 19}{8} = \frac{24}{8} = 3;\]

\[x_{2} = \frac{5 - 19}{8} = - \frac{14}{8} = - 1,75.\]

\[Ответ:x = - 1,75;x = 3.\]