Question

If A.M. between $p$ and $q$ $\left(p>q\right)$ is two times the GM, then $p:q$ is

• A. $1:1$
• B. $2:1$
• C. $\left(2+\sqrt{3}\right):\left(2-\sqrt{3}\right)$
• D. $3:1$

Answer 1

The correct option is A $1:1$

The A.M. and G.M of $p$ and $q$ is $\frac{p+q}{2}$ and $\sqrt{pq}$ respectively.

According to the problem we get,

$\frac{p+q}{2}=\sqrt{pq}$

or, $p+q-2\sqrt{pq}=0$

or, $(\sqrt{p}-\sqrt{q}{)}^2=0$

or, $\sqrt{p}=\sqrt{q}$

or, $\frac{p}{q}=1$

or, $p:q=1:1$.