Question

8b3 - a3- C3 = 3ac(a+c) prove that​

Answer 1

Given: a, b, c are in AP

∴ a + c = 2b …

(i) b = (a +  c)/2 …

(ii) Taking LHS i.e. a3 + c3 + 6abc ⇒ a3 + c3 + 6ac (a + c/2) [from (i)]

⇒ a3 + c3 + 3ac(a + c)

⇒ a3 + c3 3a2c + 3ac2

⇒ (a + c)3

⇒ (2b)3 [from (ii)] = 8b3 = RHS Hence Proved