HPT\(\Leftrightarrow\hept{\begin{cases}x=3m+2-y\\3\left(3m+2-y\right)-2y+m-11=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=3m+2-y\\-5y+10m-5=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=3m+2-\left(2m-1\right)\\y=2m-1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=m+3\\y=2m-1\end{cases}}\)
Ta co:
\(x^2-y^2=\left(m+3\right)^2-\left(2m-1\right)^2=-3m^2+10m+8=-3\left(m-\frac{5}{3}\right)^2+\frac{49}{3}\le\frac{49}{3}\)
Dau '=' xay ra khi \(m=\frac{5}{3}\)
\(\Rightarrow\left(x;y\right)=\left(\frac{14}{3};\frac{7}{3}\right)\)
Vay cap nghiem (x;y) de \(x^2-y^2\)dat max la \(\left(\frac{14}{3};\frac{7}{3}\right)\)