Complex Numbers And Quadratic Equations question 838
Question: If $ x+\frac{1}{x}=\sqrt{3}, $ then x = [RPET 2002]
Options:
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} $
D) $ \cos \frac{\pi }{6}+i\sin \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ x^{2}-\sqrt{3}x+1=0 $
Þ $ x=\frac{\sqrt{3}\pm \sqrt{3-4}}{2} $
Þ $ x=\frac{\sqrt{3}\pm i}{2} $ $ =\frac{\sqrt{3}}{2}\pm \frac{i}{2} $
Þ $ x=\cos ( \frac{\pi }{6} )+i\sin ( \frac{\pi }{6} ) $ [Taking +ve sign]
BETA
