Question

If p,q be two A.M.'s and G be one G.M. between two numbers, then $G^2=$

Answer 1

(b) (2p - q)(2q - p)

Let the two numbers be a and b

a, p, q and b are in A.P>

$\therefore p-a=q-p=b-q$

$\Rightarrow p-q=q-p$ and $q-p=b-q$

$\Rightarrow a=2p-q$ and $b=2q-p$ ..... (i)

Also, a, G and b are in G.P.

$\therefore G^2=ab$

$\Rightarrow G^2=(2p-q)(2q-p)$