Question

已知a+b=0,化简丨c-a丨+丨c-b丨+丨a+b丨

Answer 1

分类讨论：
由题意可知a = -b，即a，b互为相反数
① a >= 0 >= b，
c >= a 时，化简得 c - a + c - b + 0 =2c - (a+b) =2c
b < c < a时，化简得 a - c + c -b + 0 =a - b =2a (或 -2b)
c <= b 时，岁余化简得 a - c + b - c + 0 = (a + b) - 2c =-2c
②b > 0 > a，
c >= b 时，化简得 c - a + c - b + 0 =2c - (a+b) =2c
a < c < b时，化简得 c - a + b - c + 0 =b - a =2b (或 -2a)
c <早瞎= a 时，化陆雀空简得 a - c + b - c + 0 = (a + b) - 2c =-2c