SOLUTION: Given {{{a^2+a+1=0}}}, find the value of {{{a^1881 + a^1882 + a^1883 + ...}}} up to {{{a^1889}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Given {{{a^2+a+1=0}}}, find the value of {{{a^1881 + a^1882 + a^1883 + ...}}} up to {{{a^1889}}}      Log On


   



Question 888744: Given a%5E2%2Ba%2B1=0, find the value of a%5E1881+%2B+a%5E1882+%2B+a%5E1883+%2B+... up to a%5E1889
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If a%5E2%2Ba%2B1=0 ,then , and
, and
.
Since
then