If a, b, c are in A.P., prove that:
a3 + c3 + 6abc = 8b3
a3 + c3 + 6abc = 8b3
a3 + c3 - (2b)3 + 6abc = 0
a3 + (-2b)3 + c3 + 3a(-2b)c = 0
Since, if a + b + c = 0, a3 + b3 + c3 = 3abc
(a - 2b + c)3 = 0
a - 2b + c = 0
Since a, b, c are in AP
b - a = c - b
= a + c - 2b = 0
Hence proved