Question

已知a,b,c是有理数，a+b+c=0，abc<0,求（b+c)/|a|+(a+c)/|b|+(a+b)/|c|的值

Answer 1

a+b+c=0
a+b=-c
a+c=-b
b+c=-a

abc>0
说明a,b,c中有一个正数二个负数或a,b,c都是正数
当a,b,c中有一个正数二个负数时
(b+c)/|a| + (a+c)/|b| + (a+b)/|c|
=-a/|a| -b/|b| -c/|c
=1+1-1
=1
当a,b,c都是正数时
(b+c)/|a| + (a+c)/|b| + (a+b)/|c|
=-a/|a| -b/|b| -c/|c
=-1-1-1
=-3