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 )