Roots of the equation x3 - x + 1 = 0 are a, b, and c.
Determine the value of a16+b16+c16 !
For ax3+bx2+cx+d = 0
x1+x2+x3 = -b/a
x1 * x2 * x3= -d/a
The Attempt at a Solution
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