`P=2x^2+y^2+2xy+5x+y+37/4`
`P=(x^2+2xy+y^2)+(x+y)+(x^2+4x+4)+21/4`
`P=(x+y)^2+2(x+y). 1/2+1/4+(x+2)^2+5`
`P=(x+y+1/2)^2+(x+2)^2+5>=5`
Dấu = xảy ra khi $\begin{cases}x+y+\dfrac{1}{2}=0\\x+2=0\end{cases}$
$⇔\begin{cases}-2+y=\dfrac{-1}{2}\\x=-2\end{cases}$
$⇔\begin{cases}y=\dfrac{3}{2}\\x=-2\end{cases}$
Vậy `P_(min)=5 <=> x=-2; y=3/2`