Đáp án: $H = 16$
Giải thích các bước giải:
$\begin{array}{l}
\dfrac{a}{{2013}} = \dfrac{b}{{2012}} = \dfrac{c}{{2011}} = k\\
\Leftrightarrow \left\{ \begin{array}{l}
a = 2013k\\
b = 2012k\\
c = 2011k
\end{array} \right.\\
H = \dfrac{{{{\left( {a - c} \right)}^4}}}{{{{\left( {a - b} \right)}^2}{{\left( {b - c} \right)}^2}}}\\
= \dfrac{{{{\left( {2013k - 2011k} \right)}^4}}}{{{{\left( {2013k - 2012k} \right)}^2}{{\left( {2012k - 2011k} \right)}^2}}}\\
= \dfrac{{{{\left( {2k} \right)}^4}}}{{{k^2}.{k^2}}} = \dfrac{{16.{k^4}}}{{{k^4}}} = 16\\
Vậy\,H = 16
\end{array}$
