First slide

Theory of equations

Question

If $c \neq 0$ and the equation p/(2x) = a/(x + c) + b/(x - c) has two equal roots, then p can be

Moderate

A

$(\sqrt{a} - \sqrt{b})^{2}$
B

$(\sqrt{a} + \sqrt{b})^{2}$
C

a + b
D

a - b

Solution

We can write the given equation as
$\frac{p}{2 x} = \frac{(a + b) x + c (b - a)}{x^{2} - c^{2}}$
$\begin{array}{l} or p (x^{2} - c^{2}) = 2 (a + b) x^{2} - 2 c (a - b) x \\ or (2 a + 2 b - p) x^{2} - 2 c (a - b) x + {pc}^{2} = 0 \end{array}$
For this equation to have equal roots,
$c^{2} (a - b)^{2} - {pc}^{2} (2 a + 2 b - p) = 0$
$\begin{array}{l} or (a - b)^{2} - 2 p (a + b) + p^{2} = 0 [∵ c^{2} \neq 0] \\ or [p - (a + b)]^{2} = (a + b)^{2} - (a - b)^{2} = 4 ab \\ or p - (a + b) = \pm 2 \sqrt{ab} \\ or p = a + b \pm 2 \sqrt{ab} = (\sqrt{a} \pm \sqrt{b})^{2} \end{array}$

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