- #1

- 392

- 13

## Homework Statement

Roots of the equation x

^{3}- x + 1 = 0 are a, b, and c.

Determine the value of a

^{16}+b

^{16}+c

^{16}!

## Homework Equations

For ax

^{3}+bx

^{2}+cx+d = 0

x

_{1}+x

_{2}+x

_{3}= -b/a

x

_{1}* x

_{2}* x

_{3}= -d/a

## The Attempt at a Solution

[/B]

I know how to determine the value of a + b+ c but not a^16+b^16+c^16...

I think I can factor a^16+b^16+c^16 using binomial (Pascal's triangle) but I think it will take too much time

Such a crazy problem in a two-hour test with 100 questions and no calculator...

Please help me how to solve this easily