Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
b = \dfrac{{a + c}}{2} \Leftrightarrow 2b = a + c \Rightarrow c = 2b - a\\
\dfrac{1}{c} = \dfrac{1}{2}\left( {\dfrac{1}{b} + \dfrac{1}{d}} \right)\\
\Leftrightarrow \dfrac{1}{c} = \dfrac{1}{2}.\dfrac{{b + d}}{{bd}}\\
\Leftrightarrow \dfrac{1}{c} = \dfrac{{b + d}}{{2bd}}\\
\Leftrightarrow 2bd = c.\left( {b + d} \right)\\
\Leftrightarrow 2bd = \left( {2b - a} \right).\left( {b + d} \right)\\
\Leftrightarrow 2bd = 2{b^2} + 2bd - ab - ad\\
\Leftrightarrow 2{b^2} - ab - ad = 0\\
\Leftrightarrow b.\left( {2b - a} \right) - ad = 0\\
\Leftrightarrow b.c - ad = 0\\
\Leftrightarrow ad = bc\\
\Leftrightarrow \dfrac{a}{b} = \dfrac{c}{d}
\end{array}\)
