Q. The solution set of the equation $pqx^{2} - (p + q)^{2}x + (p + q)^{2} = 0$ is
A) $\left\{ \frac{p}{q},\ \frac{q}{p} \right\}$
B) $\left\{ pq,\ \frac{p}{q} \right\}$
C) $\left\{ \frac{q}{p},\ pq \right\}$
D) $\left\{ \frac{p + q}{p},\ \frac{p + q}{q} \right\}$
Explanation
(d)
The given equation is
$pqx^{2} - (p + q)^{2}x + (p + q)^{2} = 0$
$\therefore\ \ \ \ x = \frac{(p + q)^{2} \pm \sqrt{(p + q)^{4} - 4pq(p + q)^{2}}}{2pq}$
$\Rightarrow \ \ \ x = \frac{(p + q)^{2} \pm (p^{2} - q^{2})}{2pq}$
$\Rightarrow \ \ \ \ x = \frac{p + q}{q},\ \frac{p + q}{p}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.