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

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