Question

If (a+b+c) are not = 0
a3+ b3+ c3 = 3abc
prove that a=b=c

Answer 1

Dear student
It’s not required that a=b=c for this identity to hold true.
As we know
a3 +b3 + c3 – 3abc = (a+b+c) (a2 + b2 + c2 – ab – bc – ca)
If a+b+c = 0 , then your given statement is true
Also if a=b=c then either all are positive numbers or all should be negative numbers which cannot sum upto zero.