由(x-y)^2≥0 可得 x^2+y^2≥2xy
则x^2+y^2+2xy≥4xy
即(x+y)^2≥4xy
因为x>0,y>0,所以xy>0.x+y>0
两边同除 xy(x+y)
得(x+y)/xy≥4/(x+y),即1/x+1/y≥4/(x+y)
由(x-y)^2≥0 可得 x^2+y^2≥2xy
则x^2+y^2+2xy≥4xy
即(x+y)^2≥4xy
因为x>0,y>0,所以xy>0.x+y>0
两边同除 xy(x+y)
得(x+y)/xy≥4/(x+y),即1/x+1/y≥4/(x+y)