已知整数X 、y互为相反数,且(2x+y)(x+2y)与1/2011的相反数相等,求xy的值.

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/17 05:35:04

已知整数X 、y互为相反数,且(2x+y)(x+2y)与1/2011的相反数相等,求xy的值.
已知整数X 、y互为相反数,且(2x+y)(x+2y)与1/2011的相反数相等,求xy的值.

已知整数X 、y互为相反数,且(2x+y)(x+2y)与1/2011的相反数相等,求xy的值.
X 、y互为相反数,则x+y=0
(2x+y)(x+2y)与1/2011的相反数相等,则(2x+y)(x+2y)=-1/2011
则(x+x+y)(x+y+y)=-1/2011
(x+0)(0+y)=-1/2011
所以xy=-1/2011

因为x=-y so (2x+y)(x+2y)=(2x+(-x))(x+2(-x))=-x^2=-1/2011
所以xy=x(-x)=-x^2=-1/2011
即答案为 -1/2011

因为x和y互为相反数,所以x+y=0
(2x+y)(x+2y)=-1/2011
(x+x+y)(x+y+y)=-1/2011
(x+0)(0+y)=-1/2011
xy=-1/2011

-1/2011