Question

If $p,q$ be two AMs and G be one GM between two numbers, then $G^2$ is equal to.

• A. $(2p-q)(p-2q)$
• B. $(2p-q)(2q-p)$
• C. $(2p-q)(p+2q)$
• D. None of these

Answer 1

The correct option is B $(2p-q)(2q-p)$

Let the two numbers be $a$ and $b$

$\Rightarrow a,p,q,bϵ$A.P $\Rightarrow a=p-(q-p)=2p-q,b=q+(q-p)=2q-p...\left(1\right)$

and $a,G,bϵ$ G.P $\Rightarrow G^2=ab=(2p-q)(2q-p)$ using (1)

Hence, option 'B' is correct.