由CS不等式，易得

$$\left( \frac{a^2}{x} + \frac{b^2}{y} \right)(x+y)\geq (a+b)^2$$

当$\dfrac{a}{x}=\dfrac{b}{y}$时取等

此时有

$$\left( \frac{a^2}{x} + \frac{b^2}{y} \right)\geq \frac{(a+b)^2}{x+y}$$