已知|x-y+1|与x²+8x+16互为相反数,求x²+2xy+y²的值?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 10:30:49
![已知|x-y+1|与x²+8x+16互为相反数,求x²+2xy+y²的值?](/uploads/image/z/5303800-64-0.jpg?t=%E5%B7%B2%E7%9F%A5%7Cx-y%2B1%7C%E4%B8%8Ex%26%23178%3B%2B8x%2B16%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E6%B1%82x%26%23178%3B%2B2xy%2By%26%23178%3B%E7%9A%84%E5%80%BC%3F)
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.