若x、y为有理数,且X2+y2+1/2=x+y,求x+y
问题描述：
若x、y为有理数,且X2+y2+1/2=x+y,求x+y
答
由x^2+y^2+1/2=x+y
得(x^2-x+1/4)+(y^2-y+1/4)=0
得:(x-1/2)^2+(y-1/2)^2=0,
由于(x-1/2)^2>=0,(y-1/2)^2>=0
↔(x-1/2)^2=0,(y-1/2)^2=0,
即x=1/2,y=1/2 得x+y=1