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)


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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