First slide

Theory of equations

Question

The number of irrational roots of the equation
$4 {(x - \frac{1}{x})}^{2} + 8 (x + \frac{1}{x}) = 29$ is

Moderate

A

0
B

2
C

4
D

infinite

Solution

Put x + 1/x = t to obtain
$\begin{aligned} 4 \{t^{2} - 4\} + 8 t = 29 or 4 t^{2} + 8 t - 45 = 0 \\ \Rightarrow t^{2} + 2 t = \frac{45}{4} \Rightarrow (t + 1)^{2} = \frac{45}{4} + 1 = {(\frac{7}{2})}^{2} \end{aligned}$
$\Rightarrow t = - 1 \pm \frac{7}{2} = - \frac{9}{2}, \frac{5}{2}$
Thus, $x + \frac{1}{x} = - \frac{9}{2}, \frac{5}{2}$
$\Rightarrow x^{2} + \frac{9}{2} x + 1 = 0, x^{2} - \frac{5}{2} x + 1 = 0$
The first equation has irrational roots and the second equation has rational roots

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