Đáp án:
$\begin{array}{l}
4{a^2} + {b^2} = 5ab\\
\Rightarrow 4{a^2} - 5ab + {b^2} = 0\\
\Rightarrow 4{a^2} - 4ab - ab + {b^2} = 0\\
\Rightarrow 4a\left( {a - b} \right) - b\left( {a - b} \right) = 0\\
\Rightarrow \left( {a - b} \right)\left( {4a - b} \right) = 0\\
\Rightarrow a = b\\
\left( {do:2a > b > 0 \Rightarrow 4a > b} \right)\\
P = \dfrac{{ab}}{{4{a^2} - {b^2}}} = \dfrac{{a.a}}{{4{a^2} - {a^2}}}\\
= \dfrac{{{a^2}}}{{3{a^2}}} = \dfrac{1}{3}
\end{array}$
