ĐKXĐ: ....
\(2P=4x+y+4+4\sqrt{xy}-8\sqrt{x}-4\sqrt{y}+y-2\sqrt{y}+1+3\)
\(2P=\left(2\sqrt{x}+\sqrt{y}-2\right)^2+\left(\sqrt{y}-1\right)^2+3\ge3\)
\(\Rightarrow P_{min}=\frac{3}{2}\) khi \(\left\{{}\begin{matrix}x=\frac{1}{4}\\y=1\end{matrix}\right.\)