If A 1 ,   A 2 ;     G 1 ,   G 2 and H 1 ,   H 2 respectively be two AM's GM's and HM's between two quantities, then the value of G 1 G 2 H 1   H 2 is

Step-by-step solution

Let the two quantities be a and b , then, a ,   A 1 ,   A 2 ,   b are in A.P. ∴ A 1 - a = b - A 2       ⇒       A 1 + A 2 = a + b ......(i) Again, a ,   G 1 ,   G 2 ,   b are in GP. ∴ G 1 a = b G 2       ⇒       G 1 G 2 = a b .......(ii) Also, a ,   H 1 ,   H 2 ,   b are in HP. ∴ 1 H 1 - 1 a = 1 b - 1 H 2     ⇒       1 H 1 + 1 H 2 = 1 b + 1 a ⇒ H