First slide

Theory of equations

Question

The solution set of the equation ${pqx}^{2} - (p + q)^{2} x + (p + q)^{2} = 0$ is

Moderate

A

$\{\frac{p}{q}, \frac{q}{p}\}$
B

$\{pq, \frac{p}{q}\}$
C

$\{\frac{q}{p}, pq\}$
D

$\{\frac{p + q}{p}, \frac{p + q}{q}\}$

Solution

The given equation is ${pqx}^{2} - (p + q)^{2} x + (p + q)^{2} = 0$
$\begin{aligned} x = \frac{(p + q)^{2} \pm \sqrt{(p + q)^{4} - 4 pq (p + q)^{2}}}{2 pq} \\ x = \frac{(p + q)^{2} \pm (p^{2} - q^{2})}{2 pq} \end{aligned}$
Now, taking (+ ve) sign
$x = \frac{p + q}{q}$
$∴$ solution set is $\{\frac{p + q}{p}, \frac{p + q}{q}\}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App