Question

prove it....
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maths

Answer 1

a + b + 2c = 0

we know,

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

when, ( a + b + c ) = 0
then, a³ + b³ + c³ = 3abc

now,
LHS = a³ + b³ + 8c³
= a³ + b³ + (2c)³

we know,
here ( a + b+2c) = 0
so, according to above explanation ,
a³ + b³ + (2c)³ = 3ab(2c) = 6abc = RHS

hence ,proved //

Answer 2

a+b=-2c
Cubing both sides
a^3+b^3+3a^2b+3ab^2 = - 8c^3
a^3+b^3+8c^3=-3ab(a+b)
But a+b=-3c
So, a^3+b^3+8c^3=-3ab(-2c)=6abc