Question

a^3 b^3+c^3=3abc then a+b+c=0 or a=b=c

Prove that without using reverse method

Answer 1

we have formula

a³+b³+c³=
(a+b+c)(a²+b²+c²-ab-bc-ca) +3abc

now if a³+b³+c³=3abc
then
(a+b+c)(a²+b²+c²-ab-bc-ca) =0
either a+b+c=0
or (a²+b²+c²-ab-bc-ca) =0
which is possible only when a=b=c

Hope this helps

Answer 2

Hope This Helps You!!