QuanSiuNhan

$\dfrac{4xy}{(x+y)^2}+\dfrac{3}{2}.(\dfrac{x}{y}+\dfrac{y}{x})=(\dfrac{4xy}{(x+y)^2}+\dfrac{x^2+y^2}{2xy})+\dfrac{x^2+y^2}{xy}\geq\dfrac{4xy}{(x+y)^2}+\dfrac{(x+y)^2}{4xy}+2\geq 2+2 =4 $