Question 1151226
I think the answer needs to be 1. I think this is from "complex numbers" question if the quadratic is in the form x^2-x+1=0 the roots are -omega ,-omega^2. I think with this stuff the problem can be cracked                                     

               x+1/x=1
         =>x^2-x+1=0
         => x=-omega,-omega^2 (roots of the equation)
         Given that,
            x^1613+1/x^1613
                
               [splitting the x^1613 into (x^1611)(x^2)]

                [now replace x with -omega ]    
                   
       [ properties:- 
              
                1)omega^2+omega+1=0
                 
                2) omega^3n=1         ]      



         =>  (-omega)^1611(-omega)^2 + 1/(-omega)^1611(-omega)^2


         => -omega^2-1/omega^2
     
         =>  -(omega^4+1)/omega^2

                                   (property 2 )     
         => -(omega+1)/omega^2
                                    
         =>  -(-omega^2)/omega^2    (property 1)


         => omega^2/omega^2   => 1(ans)