Question
If ( x+frac{1}{x}=sqrt{3} ) then the value of ( x^{18}+x^{12}+x^{6}+1 ) is:

If ( x+frac{1}{x}=sqrt{3} ) then the value of ( x^{18}+x^{12}+x^{6}+1 ) is:
(A) 0
(B) 1
(C) 2
(D) 3
Solution

( if x+frac{1}{x}=sqrt{3}: x^{6}=-1 )
( (-1)^{3}+(-1)^{2}-1+1=0 )