Đáp án:
\(a = - 300;b = - 200\)
Giải thích các bước giải:
$\begin{array}{*{20}{l}}
{{{\left| {5a - 6b + 300} \right|}^{2011}} + {{\left( {2a - 3b} \right)}^{2010}} = 0}\\
{{{\left| {5a - 6b + 300} \right|}^{2011}} \ge 0 \Rightarrow |5a - 6b + 300{|^{2011}} \ge 0}\\
{{{\left( {2a - 3b} \right)}^{2010}} \ge 0}\\
{ \Rightarrow {{\left| {5a - 6b + 300} \right|}^{2011}} + {{\left( {2a - 3b} \right)}^{2010}} \ge 0}\\
{Hay\,\,{{\left| {5a - 6b + 300} \right|}^{2011}} + {{\left( {2a - 3b} \right)}^{2010}} = 0}\\
{khi\left\{ {\begin{array}{*{20}{l}}
{5a - 6b + 300 = 0}\\
{2a - 3b = 0}
\end{array}} \right.}\\
{2a - 3b = 0 \Rightarrow 2a = 3b}\\
{ \Rightarrow \frac{a}{3} = \frac{b}{2} = \frac{{5a - 6b}}{{3.5 - 2.6}} = \frac{{ - 300}}{3} = - 100}\\
{ \Rightarrow a = - 300;b = - 200}
\end{array}$
