将x^2+y^2+5/4=2x+y化为将x^2-2x+1+y^2-y+1/4=0
即(x-1)^2+(y-1/2)^2=0
上面的等式成立,则有x-1=0且y-1/2=0
即x=1,y=1/2
所以xy/(x+y)=1/2/(1+1/2)= 1/3