Q. 10 B5.0( 2 Votes )

If a, b, c are in A.P., prove that:

a3 + c3 + 6abc = 8b3

Answer :

Given: a, b, c are in AP


a + c = 2b …(i)


…(ii)


Taking Lhs i.e. a3 + c3 + 6abc


[from (i)]


a3 + c3 + 3ac(a + c)


a3 + c3 3a2c + 3ac2


(a + c)3


(2b)3 [from (ii)]


= 8b3 = RHS


Hence Proved


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