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1. 若

a 、 b 、 c

是整数, 且

|a+b|+|b+c|=1

, 则

|a-c|=

Mar 9, 2024

1. 若

a 、 b 、 c

是整数, 且

|a+b|+|b+c|=1

, 则

|a-c|=

Solution by Steps

step 1

Consider the possible values of

|a+b|

and

|b+c|

given that their sum is 1

step 2

Since

a, b,

and

c

are integers,

|a+b|

and

|b+c|

can only be 0 or 1 to satisfy

|a+b|+|b+c|=1

step 3

|a+b|=1

, then

|b+c|=0

which implies

b+c=0

. If

|b+c|=1

, then

|a+b|=0

which implies

a+b=0

step 4

From step 3, we have two cases:

step 5

Case 1: If

a+b=0

and

b+c=1

, then

a-c=a-(b+c)=a-1

. Since

|a+b|=0

a=-b

, so

|a-c|=|-b-1|=|b+1|

step 6

Case 2: If

a+b=1

and

b+c=0

, then

a-c=a-b

. Since

|b+c|=0

c=-b

, so

|a-c|=|a+b|=1

step 7

In both cases,

|a-c|

must be an integer. In Case 1,

|a-c|

could be any non-negative integer, while in Case 2,

|a-c|=1

step 8

Since the asksia-ll calculator result indicates that the solution is 'False', it suggests that there is no unique solution for

|a-c|

based on the given information

Answer

There is no unique solution for

|a-c|

based on the given information.

Key Concept

Absolute Value Properties and Integer Constraints

Explanation

The sum of the absolute values

|a+b|

and

|b+c|

being equal to 1 implies that each term must be either 0 or 1, as they are integer values. However, without additional information, we cannot determine a unique value for

|a-c|