SOLUTION: Suppose x + (1 / x) = 1 Compute the value of (x^1613) + (x^-1613) A) 1 / x B) -1 / 1613 C) x D) 1 / 1613 E) 3 F) 1 / (x^-1613) G) 2 H) 1 / (x^1613) I) none of these

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Suppose x + (1 / x) = 1 Compute the value of (x^1613) + (x^-1613) A) 1 / x B) -1 / 1613 C) x D) 1 / 1613 E) 3 F) 1 / (x^-1613) G) 2 H) 1 / (x^1613) I) none of these      Log On


   

Question 1151226: Suppose x + (1 / x) = 1
Compute the value of (x^1613) + (x^-1613)
A) 1 / x
B) -1 / 1613
C) x
D) 1 / 1613
E) 3
F) 1 / (x^-1613)
G) 2
H) 1 / (x^1613)
I) none of these
Found 2 solutions by MathLover1, pavan sai reddy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E1613+%2B+x%5E%28-1613%29

=x%5E1613+%2B+1%2Fx%5E1613

=%28x%5E1613+%2Ax%5E1613%29%2Fx%5E1613+%2B+1%2Fx%5E1613

=%28x%5E1613+%2Ax%5E1613%2B+1%29%2Fx%5E1613

=%28x%5E3226%2B+1%29%2Fx%5E1613

=%28x%5E3226%2B+1%29%2Fx%5E1613

so, your answer is: I) none of these


Answer by pavan sai reddy(3) About Me  (Show Source):
You can put this solution on YOUR website!
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)