\(P=\dfrac{xy}{x^2+y^2}=\dfrac{4}{17}-\dfrac{1}{17}\left(4x^2-17xy+4y^2\right)\le\dfrac{4}{17}-\dfrac{1}{17}\left[\left(\dfrac{x^2}{4}-2xy+4y^2\right)+\dfrac{15}{4}x^2-15x+15\right]\)
\(=\dfrac{4}{17}-\dfrac{1}{17}\left[\left(\dfrac{x}{2}-2y\right)^2+\dfrac{15}{4}\left(x-2\right)^2\right]\le\dfrac{4}{17}\)
Dâu = xảy ra khi \(x=2;y=\dfrac{1}{2}\)