\[\boxed{\mathbf{1145}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]
\[\frac{x² - 2\text{ax} + 3}{x - 2} = 0\]
\[x \neq 2\]
\[x^{2} - 2\text{ax} + 3 = 0\]
\[D = 4a^{2} - 12 = 0\]
\[4a^{2} - 12 = 0\]
\[a^{2} = 3\]
\[a = \pm \sqrt{3}\]
\[Ответ:\ при\ a = \pm \sqrt{3}.\]