（x+y)/2与(x+y)/xy用比商法怎么比较大小?
问题描述：
（x+y)/2与(x+y)/xy用比商法怎么比较大小?
就是比较大小,不用加减法比较,那我会,但用比商法我不会,老师讲时我没听见..
答
X+Y/2与XY/X+Y (X>O,Y>O）(X+Y)/2=(X+Y)^2/[2(X+Y)]=(X^2+2XY+Y^2)/[2(X+Y)]=(X^2+Y^2)/[2(X+Y)]+2XY/[2(X+Y)]XY/(X+Y)=2XY/[2(X+Y)]∵(X^2+Y^2)/[2(X+Y)]+2XY/[2(X+Y)]＞2XY/[2(X+Y)]∴(X+Y)/2＞XY/(X+...