已知x,y均为正数,且x>y,求证：2x+1/(x2-2xy+y2)>=2y+3

已知x,y均为正数,且x>y,求证：2x+1/(x2-2xy+y2)>=2y+3
已知x,y均为正数,且x>y,求证：2x+1/(x2-2xy+y2)>=2y+3

已知x,y均为正数,且x>y,求证：2x+1/(x2-2xy+y2)>=2y+3
设x=y+z(z>0)
则原式=2（y+z）+1/(z^2)=2y+2z+1/(z^2)=2y+z+z+1/(z^2)
而（z+z+1/(z^2)）/3》1（三项均值）
故原式=2y+z+z+1/(z^2)》2y+3