Quote:
In the question, it is not mentioned that "a" or "b" is a constant …
a and
b are variables.
Quote:
… " |a| + |b| = 0 " does not guarantee that a and b are "0" …
Any absolute value is non-negative. If
a and
b were not zeroes, then |
a| would be positive and |
b| would be positive.
positive + positive > 0
That would contradict the equation. Even if only one variable was not zero, the left side would still be positive. So the both variables can possess only one value, 0.
Quote:
… It could mean a = -b.
If to plug in
a = -
b we will get |-
b| + |
b| as the left side of the equation. It is not necessarily 0. Plug any non-zero value for
b, for example
b = 2 yields |-2| + |2| = 2 + 2 = 4. So the conclusion "It could mean
a = -
b" is not correct.
If to solve the equation |-
b| + |
b| = 0:
The absolute values |-
b| and |
b| are the same (equal), so the equation transforms into
2|
b| = 0
b = 0