\[\boxed{\mathbf{691\ (691).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[Уравнение\ не\ имеет\ корней\ \]
\[при\ D < 0.\]
\[1)\ x² + mx + m² + 1 = 0\]
\[D = m^{2} - 4 \cdot \left( m^{2} + 1 \right) =\]
\[= m^{2} - 4m^{2} - 4 =\]
\[= - 3m^{2} - 4 < 0\]
\[2)\ x² - 2mx + 2m^{2} + 9 = 0\]
\[D = 4m^{2} - 4 \cdot \left( 2m^{2} + 9 \right) =\]
\[= 4m^{2} - 8m^{2} - 36 =\]
\[= - 4m^{2} - 36 < 0\]