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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

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Solution

(a) (2p − q) (p − 2q)

Let the two numbers be a and b.a, p, q and b are in A.P. p-a=q-p=b-q p-a=q-p and q-p=b-qa=2p-q and b= 2q-p (i)Also, a, G and b are in G.P. G2=abG2=2p-q2q-p

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