If x + frac{1}{x} = sqrt{3}, then x = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $x + \frac{1}{x} = \sqrt{3}$.Multiplying by $x$,we get $x^2 - \sqrt{3}x + 1 = 0$.Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4

Vedclass · Accepted Answer

$\cos \frac{\pi}{6} + i \sin \frac{\pi}{6}$

Vedclass · Answer

(D) Given $x + \frac{1}{x} = \sqrt{3}$.Multiplying by $x$,we get $x^2 - \sqrt{3}x + 1 = 0$.Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$,we have:$x = \frac{\sqrt{3} \pm \sqrt{(\sqrt{3})^2 - 4(1)(1)}}{2(1)}$$x = \frac{\sqrt{3} \pm \sqrt{3 - 4}}{2} = \frac{\sqrt{3} \pm \sqrt{-1}}{2} = \frac{\sqrt{3} \pm i}{2}$.Thus,$x = \frac{\sqrt{3}}{2} \pm \frac{i}{2}$.Taking the positive sign,$x = \frac{\sqrt{3}}{2} + i \frac{1}{2} = \cos \frac{\pi}{6} + i \sin \frac{\pi}{6}$.

If $x + \frac{1}{x} = \sqrt{3},$ then $x =$

Similar Questions

$\left| {(1 + i)\frac{{(2 + i)}}{{(3 + i)}}} \right| = $

If ${z_1}$ and ${z_2}$ are two complex numbers,then $|{z_1} + {z_2}|$ is

If $Z = \frac{(\sqrt{3} + i)^{3}(3i + 4)^{2}}{(8 + 6i)^{2}}$,then $|Z|$ is equal to

If $\alpha$ and $\beta$ are different complex numbers with $|\beta|=1,$ then find $\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|.$

If the conjugate of $(x + iy)(1 - 2i)$ is $1 + i$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module