已知X∈R,Y＞0,集合A=﹛X²+X+1,-X,X-1﹜集合B=﹛-y,-y/2,y+1﹜若A=B,则x²+y²的值?

已知X∈R,Y＞0,集合A=﹛X²+X+1,-X,X-1﹜集合B=﹛-y,-y/2,y+1﹜若A=B,则x²+y²的值?
已知X∈R,Y＞0,集合A=﹛X²+X+1,-X,X-1﹜集合B=﹛-y,-y/2,y+1﹜若A=B,
则x²+y²的值?

已知X∈R,Y＞0,集合A=﹛X²+X+1,-X,X-1﹜集合B=﹛-y,-y/2,y+1﹜若A=B,则x²+y²的值?
因为Y>0,所以-y与-y/2均小于零,而X2+X+1=(X+0.5)2+0.75>0,所以y+1=X2+X+1,若-x=-y,则经计算X=Y=0,则-Y=-Y/2,不满足集合的性质,所以Y=2X,X-1=-Y,解得X=1/3,Y=2/3,所以X2+Y2=5/9.

X=1/3y=2/3 答案5/9