\[{\text{Решить уравнение:}}\]
$%{\text{6}} \cdot {{\text{4}}^{\frac{1}{{{x^2}}}}} - 13 \cdot {6^{\frac{1}{{{x^2}}}}} + 6 \cdot {9^{\frac{1}{{{x^2}}}}} = 0$%
\[{\text{Разделите уравнение на }}{9^{\frac{1}{{{x^2}}}}}.\]
\[\begin{array}{l}{\text{Разделим уравнение на }}{9^{\frac{1}{{{x^2}}}}}.{\text{ Получаем}}\\{\text{6}} \cdot {\left( {\frac{{\text{4}}}{9}} \right)^{\frac{1}{{{x^2}}}}} - 13 \cdot {\left( {\frac{2}{3}} \right)^{\frac{1}{{{x^2}}}}} + 6 = 0\\{\text{Делаем замену }}{\left( {\frac{2}{3}} \right)^{\frac{1}{{{x^2}}}}} = t\\6{t^2} - 13t + 6 = 0 \Leftrightarrow \left[ \begin{array}{l}t = \frac{3}{2}\\t = \frac{2}{3}\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}{\left( {\frac{2}{3}} \right)^{\frac{1}{{{x^2}}}}} = {\left( {\frac{2}{3}} \right)^{ - 1}}\\{\left( {\frac{2}{3}} \right)^{\frac{1}{{{x^2}}}}} = \frac{2}{3}\end{array} \right. \Leftrightarrow \\\left[ \begin{array}{l}\frac{1}{{{x^2}}} = - 1{\text{ решений нет}}\\\frac{1}{{{x^2}}} = 1\end{array} \right. \Leftrightarrow {x^2} = 1 \Leftrightarrow x = \pm 1.\end{array}\]
\[x = \pm 1\]
