Đáp án:
$\begin{array}{l}
1)\dfrac{a}{c} = \dfrac{c}{b} \Rightarrow {c^2} = a.b\\
\dfrac{{{a^2} + {c^2}}}{{{b^2} + {c^2}}} = \dfrac{{{a^2} + a.b}}{{{b^2} + ab}} = \dfrac{{a\left( {a + b} \right)}}{{b\left( {a + b} \right)}} = \dfrac{a}{b}\\
2)\\
{b^2} = a.c\\
\Rightarrow \dfrac{a}{b} = \dfrac{b}{c} = \dfrac{{2012b}}{{2012c}}\\
= \dfrac{{a + 2012b}}{{b + 2012c}}\\
\Rightarrow {\left( {\dfrac{a}{b}} \right)^2} = {\left( {\dfrac{{a + 2012b}}{{b + 2012c}}} \right)^2}\\
\Rightarrow \dfrac{a}{b}.\dfrac{b}{c} = {\left( {\dfrac{{a + 2012b}}{{b + 2012c}}} \right)^2}\\
\Rightarrow \dfrac{a}{c} = {\left( {\dfrac{{a + 2012b}}{{b + 2012c}}} \right)^2}
\end{array}$
