Whoo!!! another super tricky question which can take you off the hooks during exam.
The simplest way to look at this question is we have 3 conditions a>0, b>0 and c>0 so thy are positive numbers but can be integers or fraction. (always proceed with this thought process - even if irrelevant here, it helps in the long run).
Question asks if a(b-c)=0 now we know a>0 thus a not equal to 0 hence b-c=0 or B=C
Statement 1
B-c=0
B=c Sufficient
Statement 2
c^2=B^2
|C|=|B|
since they are both greater than 0 hence c=b
Suffcienet
Answer is D.
+kudos I need to unlock the exams