若x>y>0,xy=1,求x눀+y눀⼀x-y的最小值

2024-12-03 08:37:48
推荐回答(3个)
回答1:

x²+y²/x-y
=(x+y)(x-y)/(x-y)
=x+y
>=2根号xy=2

回答2:



楼主再算算

回答3:

(x^2+y^2)/(x+y)=[(x-y)^2+2xy]/(x-y)=(x-y)+2/(x-y)≥2根号(2)
当且仅当x-y=2/(x-y)时,取等号!