Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{\left( {2x - 5} \right)^{2018}} \ge 0,\,\,\,\,\forall x\\
{\left( {3y + 4} \right)^{2020}} \ge 0,\,\,\,\,\forall y\\
\Rightarrow {\left( {2x - 5} \right)^{2018}} + {\left( {3y + 4} \right)^{2020}} \ge 0,\,\,\,\,\forall x,y
\end{array}\)
Từ giả thiết suy ra \(\left\{ \begin{array}{l}
{\left( {2x - 5} \right)^{2018}} = 0\\
{\left( {3y + 4} \right)^{2020}} = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = \frac{5}{2}\\
y = - \frac{4}{3}
\end{array} \right.\)
Ta có:
\(\begin{array}{l}
M + \left( {5{x^2} - 2xy} \right) = 6{x^2} + 9xy - {y^2}\\
\Leftrightarrow M = {x^2} + 11xy - {y^2} = {\left( {\frac{5}{2}} \right)^2} + 11.\frac{5}{2}.\frac{{ - 4}}{3} - {\left( {\frac{{ - 4}}{3}} \right)^2} = \frac{{ - 1159}}{{36}}
\end{array}\)
