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+Y)
（x+y)/2与(x+y)/xy用比商法怎么比较大小?
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+Y)