\[\boxed{\text{767.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[12x^{2} + 70x + a^{2} + 1 = 0\ \ |\ :12\]
\[x^{2} + \frac{70}{12}x + \frac{a^{2} + 1}{12} = 0\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = - \frac{70}{12} \\ x_{1}x_{2} = \frac{a^{2} + 1}{12} \\ \end{matrix} \right.\ \]
\[так\ как\ - \frac{70}{12} < 0,\ то\ x_{1} < 0,\ \]
\[x_{2} < 0\ или\ x_{1} < 0,\ x_{2} > 0;\]
\[так\ как\ \frac{a^{2} + 1}{12} > 0,\ то\ x_{1} < 0;\ \]
\[x_{2} < 0 - что\ и\ требовалось\ \]
\[доказать.\ \]