Question

If p, q be two A.M.’s and G be one G.M. between two numbers, then G² =

A. (2p - q)(p - 2q)

B. (2p - q)(2q - p)

C. (2p - q)(p+2q)

D. none of these

Answer 1

Let the numbers be a,b.

∴ a,p,q,b (two A.M.)

⇒ a,G,b(one GM)

G² = a.b(GM)

2p = a+q(AM)

2q = b+p(AM)

a = 2p - q

b = 2q - p

∴ a.b = (2p - q)(2q - p)

G² = (2p - q)(2q - p)