已知x,y满足等式2x+x²+x²y²+2=-2xy,那么x+y的值是

已知x,y满足等式2x+x²+x²y²+2=-2xy,那么x+y的值是
已知x,y满足等式2x+x²+x²y²+2=-2xy,那么x+y的值是

已知x,y满足等式2x+x²+x²y²+2=-2xy,那么x+y的值是
解
2x+x²+x²y²+2=-2xy
(x²y²+2xy+1)+(x²+2x+1)=0
(xy+1)²+(x+1)²=0
∴xy+1=0,x+1=0
∴x=-1,y=1
∴x+y=-1+1=0