Giải thích các bước giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\begin{array}{l}
\dfrac{a}{b} = \dfrac{c}{d} \Leftrightarrow \dfrac{a}{c} = \dfrac{b}{d}\\
\Leftrightarrow {\left( {\dfrac{a}{c}} \right)^2} = {\left( {\dfrac{b}{d}} \right)^2}\\
\Leftrightarrow \dfrac{{{a^2}}}{{{c^2}}} = \dfrac{{{b^2}}}{{{d^2}}} = \dfrac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}} = \dfrac{{{a^2} - {b^2}}}{{{c^2} - {d^2}}}\\
\dfrac{a}{c} = \dfrac{b}{d} = \dfrac{{a - b}}{{c - d}} \Leftrightarrow {\left( {\dfrac{a}{c}} \right)^2} = {\left( {\dfrac{{a - b}}{{c - d}}} \right)^2}\\
{\left( {\dfrac{a}{c}} \right)^2} = \dfrac{a}{c}.\dfrac{a}{c} = \dfrac{a}{c}.\dfrac{b}{d} = \dfrac{{ab}}{{cd}}\\
\Rightarrow \dfrac{{ab}}{{cd}} = {\left( {\dfrac{{a - b}}{{c - d}}} \right)^2} = {\left( {\dfrac{a}{c}} \right)^2} = \dfrac{{{a^2}}}{{{c^2}}} = \dfrac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}} = \dfrac{{{a^2} - {b^2}}}{{{c^2} - {d^2}}}\\
\Rightarrow \dfrac{{ab}}{{cd}} = \dfrac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}} = \dfrac{{{a^2} - {b^2}}}{{{c^2} - {d^2}}} = {\left( {\dfrac{{a - b}}{{c - d}}} \right)^2}
\end{array}\)
