If x+1 x =3, then x= - Vidyadip

MCQ

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

A
$\cos \frac{\pi}{3}+ i \sin \frac{\pi}{3}$
B
$\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}$
C
$\sin \frac{\pi}{6}+i \cos \frac{\pi}{6}$
✓
$\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}$

✓

Answer

Correct option: D.

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

(D)
$x^2-\sqrt{3} x+1=0$
$\Rightarrow x=\frac{\sqrt{3} \pm \sqrt{3-4}}{2}$
$\Rightarrow x=\frac{\sqrt{3} \pm i }{2}=\frac{\sqrt{3}}{2} \pm \frac{ i }{2}$
$\Rightarrow x=\cos \left(\frac{\pi}{6}\right)+ i \sin \left(\frac{\pi}{6}\right)$ [Taking + ve sign ]

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