Question

If one $AM 'A'$ and two $GM$ $p$ and $q$ are inserted between two given numbers, then find the value of $\frac{p^{2}}{q}+\frac{q^{2}}{p}$

• A. $A$
• B. $2A$
• C. $3A$
• D. $4A$

Answer 1

Answer: (B)

Let $a$ and $b$ are two numbers.
Then, $A=\frac{a+b}{2} \ldots(i)$
Also, $a, p, q, b$ are in $G P$.
$\frac{p}{a}=\frac{q}{a}=\frac{b}{q}$
$\Rightarrow \frac{p^{2}}{q}=a$ and $\frac{q^{2}}{p}=b$
$\therefore \frac{p^{2}}{q}+\frac{q^{2}}{p}=a+b=2 A$ [Using eq. (i)]