Let ABC be a non-zero rational number, find that c of |a|part a+|b|part b+|c| is equal to?

Let ABC be a non-zero rational number, find that c of |a|part a+|b|part b+|c| is equal to?

A =1 or -1
B =1 or -1
C =1 or -1
So
|A|a+b|b+c|c
=1+1+1=3
Or =-1-1-1=-3
Or =1+1-1=1
Or 1-1-1=-1

A =1 or -1
B =1 or -1
C =1 or -1
So
|A|a+b|b+c|c
=1+1+1=3
Or =-1-1-1=-3
OR =1+1-1=1
Or 1-1-1=-1

If the rational a.b.c satisfies abc not equal to 0, find the sum of the squares of all possible values of a/|a b/|b c/|c|

There are two scenarios
1 Abc >0
Then all positive or two negative and one positive
A/|a b/|b c/|c|=1+1+1=3
A/|a b/|b c/|c|=-1-1+1=-1
2 Abc <0
Then all negative or two positive and one negative
A/|a b/|b c/|c|=-1-1-1=-3
A/|a b/|b c/|c|=-1+1+1=1
A:1,-1,-3, or the sum of the squares of 3 is:1+1+9+9=20