已知x>0,y>0,且xy-(x+y)=1,求证x+y>=2(根号2+1)

问题描述:

已知x>0,y>0,且xy-(x+y)=1,求证x+y>=2(根号2+1)

xy-x-y+1=2,(x-1)(y-1)=2 x-1+y-1>=2√(x-1)(y-1)=2√2 x+y>=2√2+2=2(√2+1)