Найдите корни уравнения: (x*корень из 7)/(x*корень из 7-корень из2)=(x*корень из 2)/(корень из 7-x*корень из 2).

\[\frac{x\sqrt{7}}{x\sqrt{7} - \sqrt{2}} = \frac{x\sqrt{2}}{\sqrt{7} - x\sqrt{2}}\]

\[ОДЗ:\]

\[1)\ x\sqrt{7} - \sqrt{2} \neq 0\]

\[x\sqrt{7} \neq \sqrt{2}\]

\[x \neq \frac{\sqrt{2}}{\sqrt{7}}\]

\[2)\ \sqrt{7} - x\sqrt{2} \neq 0\]

\[x\sqrt{2} \neq \sqrt{7}\]

\[x \neq \frac{\sqrt{7}}{\sqrt{2}}\]

\[x\sqrt{7}\left( \sqrt{7} - x\sqrt{2} \right) =\]

\[= x\sqrt{2}\left( x\sqrt{7} - \sqrt{2} \right)\]

\[7x - x^{2}\sqrt{14} = x^{2}\sqrt{14} - 2x\]

\[- 2\sqrt{14}x^{2} + 9x = 0\]

\[x\left( - 2\sqrt{14}\ x + 9 \right) = 0\]

\[x = 0\ \ \ \ \ \ \ \ \ - 2\sqrt{14}x + 9 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - 2\sqrt{14}x = 9\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{- 9}{- 2\sqrt{14}} = \frac{9\sqrt{14}}{28}\]

\[Ответ:\ x = 0;\ \ \ \ \ \ x = \frac{9\sqrt{14}}{28}.\]