Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{a^2}.{b^2} = {\left( {a.b} \right)^2}\\
1,\\
36{\left( {4x - 1} \right)^2} = 25.{\left( {3x + 2} \right)^2}\\
\Leftrightarrow {6^2}.{\left( {4x - 1} \right)^2} = {5^2}.{\left( {3x + 2} \right)^2}\\
\Leftrightarrow {\left( {24x - 6} \right)^2} = {\left( {15x + 10} \right)^2}\\
\Leftrightarrow \left[ \begin{array}{l}
24x - 6 = 15x + 10\\
24x - 6 = - \left( {15x + 10} \right)
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
9x = 16\\
39x = - 4
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{{16}}{9}\\
x = - \frac{4}{{39}}
\end{array} \right.\\
2,\\
49.{\left( {2 - 3x} \right)^2} = 9.{\left( {\frac{2}{3} + 4x} \right)^2}\\
\Leftrightarrow {7^2}.{\left( {2 - 3x} \right)^2} = {3^2}.{\left( {\frac{2}{3} + 4x} \right)^2}\\
\Leftrightarrow {\left( {14 - 21x} \right)^2} = {\left( {2 + 12x} \right)^2}\\
\Leftrightarrow \left[ \begin{array}{l}
14 - 21x = 2 + 12x\\
14 - 21x = - 2 - 12x
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
33x = 12\\
9x = 16
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{4}{{11}}\\
x = \frac{{16}}{9}
\end{array} \right.\\
3,\\
16.{\left( {\frac{1}{7} + x} \right)^2} = 81.{\left( {\frac{3}{2}x - 2} \right)^2}\\
\Leftrightarrow {4^2}.{\left( {\frac{1}{7} + x} \right)^2} = {9^2}.{\left( {\frac{3}{2}x - 2} \right)^2}\\
\Leftrightarrow {\left( {\frac{4}{7} + 4x} \right)^2} = {\left( {\frac{{27}}{2}x - 18} \right)^2}\\
\Leftrightarrow \left[ \begin{array}{l}
\frac{4}{7} + 4x = \frac{{27x}}{2} - 18\\
\frac{4}{7} + 4x = 18 - \frac{{27}}{2}x
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{{260}}{{133}}\\
x = \frac{{244}}{{245}}
\end{array} \right.
\end{array}\)
