(1+1/x)(1+1/y)=1+1/x+1/y+1/xy=1+(x+y)/x+(x+y)/y+(x+y)²/xy=1+1+y/x+1+x/y+x/y+2+y/x=5+2(y/x+x/y)>=5+2×2√y/x*x/y=5+4=9最小值=9
4xy<=(x+y)^2=1, xy<=1/4(1+1/x)(1+1/y)=(x+1)(y+1)/xy=(2+xy)/xy=1+2/xy>=1+8=9