求证明不等式...1/x+1/y大于或等于4/x+y ...

网友回答

就柯西不等式啊
(1/x+1/y)(x+y)>=(1+1)^2=4
故1/x+1/y>=4/(x+y)
======以下答案可供参考======
供参考答案1:
貌似这个不等式不成立吧
供参考答案2:
1/x+1/y-4/(x+y)=[y(x+y)+x(x+y)-4xy]/[xy(x+y)]
=[x²-2xy+y²]/[xy(x+y)]=(x-y)²/[xy(x+y)]≥0
∴1/x+1/y≥4/(x+y)