令x y=a,则有a a/(xy)=5,xy=a/(5-a),利用均值不等式,有a=x y>=2sqrt(xy),a^2>=4a/(5-a),又因为x>0,y>0,所以xy>0,a>0.所以5-a>0.则a^3-5a^2 4a<=0,(a-4)(a-1)<=0.所以a-4>=0,a-1<=0(舍去)或a-4<=0,a-1>=0.即1<=a<=4.所以(x y) max=a max=4.
