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?
互为相反数则相加为0
|x-y+1|+x²+8x+16=0
|x-y+1|+(x+4)²=0
绝对值和平方大于等于0
相加等于0,若有一个大于0,则另一个小于0,不成立.
所以两个都等于0
所以x-y+1=0
x+4=0
x=-4,y=x+1=-3
所以x²+2xy+y²
=(x+y)²
=(-4-3)²
=49

|X-Y+1|>=0, X^2+8X+16=(X+4)^2>=0.
它们互为相反数只能等于0。
X+1-Y=0
X+1=Y
X^2+2XY+Y^2=(X+Y)^2=(2X+1)^2=(2*-4+1)^2=49.