15.若m,n均为整数,且|m-3|+|m-n|=1,则m+n=____

2025-06-28 01:45:08
推荐回答(1个)
回答1:

|m-3|+|m-n|=1

case 1: |m-3|=0  => m=3

|m-3|+|m-n|=1

0+|3-n|=1

|3-n|=1

3-n = 1 or -1

n=4 or 2

m+n= 7 or 5

case 2: |m-3|=1  =>m=4 or 2

m=4

|m-3|+|m-n|=1

|4-3|+|4-n| =1

|4-n| =0

n=4

m+n =4+4=8

m=2

|m-3|+|m-n|=1

|2-3|+|2-n|=1

|2-n|=0

n=2

m+n= 2+2=4

ie

m+n=7 or 5 or 8 or 4