已知|x-y+1|与x²+8x+16互为相反数,求x²+2xy+y²的值

已知|x-y+1|与x²+8x+16互为相反数,求x²+2xy+y²的值
已知|x-y+1|与x²+8x+16互为相反数,求x²+2xy+y²的值

已知|x-y+1|与x²+8x+16互为相反数,求x²+2xy+y²的值

由题意有
|x-y+1| + x²+8x+16=0 ==> |x-y+1|+ (x+4)² = 0
因此：
x-y+1 = 0
x+4 = 0
解得：x=-4；y= -3
则： x²+2xy+y² = (x+y)² = 49