Question

有理数x,y满足（x-y)的平方+x的平方+2x+1=0,则（xy)2005次方

Answer 1

(X-Y)^2+X^2+2X+1=0

(X-Y)^2+(X+1)^2=0

(X-Y)^2=-(X+1)^2,因为一个正数等于一个负数,只可能是零,所以

(X-Y)^2=0,(X+1)^2=0,则X=Y=-1

(XY)2005=1