\(P\ge\frac{1}{2}\left(2x+\frac{1}{x}+2y+\frac{1}{y}\right)^2=\frac{1}{2}\left[2\left(x+y\right)+\frac{1}{x}+\frac{1}{y}\right]^2=\frac{1}{2}\left(2+\frac{1}{x}+\frac{1}{y}\right)^2\)
\(P\ge\frac{1}{2}\left(2+\frac{4}{x+y}\right)^2=\frac{1}{2}\left(2+4\right)^2=18\)
\(\Rightarrow P_{min}=18\) khi \(x=y=\frac{1}{2}\)