Q5 of 167 Page 19

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


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