\[\begin{array}{l}
b\left( {{b^2} - {a^2}} \right) = c\left( {{c^2} - {a^2}} \right)\\
\Leftrightarrow {b^3} - b{a^2} = {c^3} - c{a^2}\\
\Leftrightarrow {b^3} - {c^3} - \left( {b{a^2} - c{a^2}} \right) = 0\\
\Leftrightarrow \left( {b - c} \right)\left( {{b^2} + bc + {c^2}} \right) - {a^2}\left( {b - c} \right) = 0\\
\Leftrightarrow \left( {b - c} \right)\left( {{b^2} + bc + {c^2} - {a^2}} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
b - c = 0\\
{b^2} + bc + {c^2} = {a^2}
\end{array} \right.\,\,\,\\
+ )\,\,\,b - c = 0 \Leftrightarrow b = c \Rightarrow \Delta ABC\,\,can\,\,\,tai\,\,A.\\
+ )\,\,{b^2} + bc + {c^2} = {a^2} \Leftrightarrow {b^2} + {c^2} - {a^2} = - bc\\
Ta\,\,co:\,\,\,\cos A = \frac{{{b^2} + {c^2} - {a^2}}}{{2bc}} = \frac{{ - bc}}{{2bc}} = - \frac{1}{2}\\
\Rightarrow \cos A = - \frac{1}{2} \Rightarrow \angle A = {120^0}.
\end{array}\]
