x>y>0且xy=1求证（x^2+y^2)/(x-y)>=2√2,并且求等号成立的条件

x>y>0且xy=1求证（x^2+y^2)/(x-y)>=2√2,并且求等号成立的条件
x>y>0且xy=1求证（x^2+y^2)/(x-y)>=2√2,并且求等号成立的条件

x>y>0且xy=1求证（x^2+y^2)/(x-y)>=2√2,并且求等号成立的条件
因为x>y,x-y>0,左边=[(x-y)~2+2xy]/(x-y)=x-y+2xy/(x-y)=(x-y)+2/(x-y)>=2根号[(x-y)*2/(x-y)]=2根号2