1/x+1/y=(1/x+1/y)(x+2y)因为x+2y=1=1+2y/x+x/y+2x>0,y>0,所以2y/x+x/y>=2√(2y/x*x/y)=2√2当2y/x=x/y时取等号x^2=2y^2x=√2y√2y+2y=1,有正数解所以等号能取到所以1/x+1/y=1+2y/x+x/y+2>=3+2√2所以最小值=3+2√2
