First slide

Theory of expressions

Question

Sum of the roots of the equation
$4 {(x - \frac{1}{x})}^{2} - 4 (x - \frac{1}{x}) + 1 = 0$ is

Moderate

A

5
B

1
C

– 5/2
D

-1

Solution

Put $x - \frac{1}{x} = t$ to obtain $4 t^{2} - 4 t + 1 = 0$
$\Rightarrow t = \frac{1}{2}, \frac{1}{2}$
Now, $x - \frac{1}{x} = \frac{1}{2} \Rightarrow \frac{x^{2} - 1}{x} = \frac{1}{2}$
$\Rightarrow 2 x^{2} - x - 2 = 0$
$∴$ Sum of roots of the given equation $= \frac{1}{2} + \frac{1}{2} = 1$

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