Đáp án:
$\begin{array}{l}
{a^2} = 2ab + 3{b^2}\\
\Rightarrow {a^2} - 2ab - 3{b^2} = 0\\
\Rightarrow {a^2} - 3ab + ab - 3{b^2} = 0\\
\Rightarrow a\left( {a - 3b} \right) + b\left( {a - 3b} \right) = 0\\
\Rightarrow \left( {a + b} \right)\left( {a - 3b} \right) = 0\\
\Rightarrow a = 3b\left( {do:a < b < 0} \right)\\
P = \dfrac{{{a^3} + {a^2}b + a{b^2} + {b^3}}}{{{a^2} - {b^3}}}\\
= \dfrac{{{{\left( {3b} \right)}^3} + {{\left( {3b} \right)}^2}.b + 3b.{b^2} + {b^3}}}{{{{\left( {3b} \right)}^3} - {b^3}}}\\
= \dfrac{{27{b^3} + 9{b^3} + 3{b^3} + {b^3}}}{{26{b^3}}}\\
= \dfrac{{40{b^3}}}{{26{b^3}}}\\
= \dfrac{{20}}{{13}}
\end{array}$
