\(P=\left(4x^2+y^2+1-4xy-4x+2y\right)+4\left(y^2+4y+4\right)-69\)
\(=\left(2x-y-1\right)^2+4\left(y+2\right)^2-69\ge-69\)
\(P_{min}=-69\) khi \(\left\{{}\begin{matrix}2x-y-1=0\\y+2=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{2}\\y=-2\end{matrix}\right.\)
\(P=4x^2-4xy+5y^2-4x+18y-52\)
\(P=\left(4x^2-4xy+y^2\right)+\left(4y^2+16y+16\right)-4x+2y-68\)
\(P=\left(2x-y\right)^2+\left(2y+4\right)^2-2\left(2x-y\right)-68\)
\(P=\left[\left(2x-y\right)^2-2\left(2x-y\right)+1\right]+\left(2y+4\right)^2-69\)
\(P=\left(2x-y+1\right)^2+\left(2y+4\right)^2-69\ge-69\)
Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}2x-y+1=0\\2y+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{3}{2}\\y=-2\end{matrix}\right.\)
Vậy \(Min_P=-69\) khi \(\left(x;y\right)=\left(-\dfrac{3}{2};-2\right)\)
