\[\boxed{\mathbf{687\ (687).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ 6x² + 5x - \frac{1}{x + 1} = 1 - \frac{1}{x + 1}\]
\[6x^{2} + 5x - \frac{1}{x + 1} - 1 + \frac{1}{x + 1} = 0,\ \ \]
\[x + 1 \neq 0;\ \ x \neq - 1\]
\[6x^{2} + 5x - 1 = 0\]
\[D = 25 + 24 = 49\]
\[x = \frac{- 5 \pm 7}{12}\]
\[x_{1} = - 1\ (не\ подходит);\ \ \ x_{2} = \frac{1}{6}\]
\[Ответ:x = \frac{1}{6}.\]
\[2)\ 5x² - 14 \cdot \left( \sqrt{x} \right)^{2} - 3 = 0\]
\[5x^{2} - 14x - 3 = 0,\ \ x \geq 0\]
\[D = 196 + 4 \cdot 15 = 256\]
\[x = \frac{14 \pm 16}{10}\]
\[x_{1} = 3;\ \ \ \ \ x_{2} = - \frac{1}{5}\ (не\ подходит)\]
\[Ответ:x = 3.\]