if a³+b³+c³=3abc,prove that either a+b+c=0 or a=b=c
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Answer:
We know,
a
3
+b
3
+c
3
−3abc=(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
Putting a+b+c=0 on RHS, we get,
a
3
+b
3
+c
3
−3abc=0
⟹a
3
+b
3
+c
3
=3abc, Hence proved
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