Question

如果x的二次方y的二次方减去4xy,加x的平方,加y的平方加1等于零,那么x+y=?

Answer 1

x^2y^2-4xy+x^2+y^2+1= (xy)^2-2xy+1 +x^2-2xy+y^2=(xy-1)+(x-y)^2=0

xy-1=0,x-y=0,x^2=y^2=1,x=y=1 或x=y=-1

x+y=2 或x+y=-2