若丨x-y+1丨与丨x+y-2013丨互为相反数,求(x+2y)/(x-y)的值

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若丨x-y+1丨与丨x+y-2013丨互为相反数,求(x+2y)/(x-y)的值
若丨x-y+1丨与丨x+y-2013丨互为相反数,求(x+2y)/(x-y)的值

若丨x-y+1丨与丨x+y-2013丨互为相反数,求(x+2y)/(x-y)的值
∵丨x-y+1丨与丨x+y-2013丨互为相反数
∴|x-y+1|+|x+y-2013|=0
∴x-y+1=0,x+y-2013=0
∴x=1006,y=1007
∴(x+2y)/(x-y)
=(1006+2014)/(1006-1007)
=-3020

因为丨x-y+1丨≥0,丨x+y-2013丨≥0,并且丨x-y+1丨与丨x+y-2013丨互为相反数
所以丨x-y+1丨=丨x+y-2013丨=0
x-y+1=0
x+y-2013=0
解得,x=1006,y=1007
(x+2y)/(x-y)
=-3020

绝对值大于等于0,又互为相反数,所以只能是0了,所以x-y+1=0,x+y-2013=0,x=1006,y=1007,所以答案为-3020