Question Number 1050 by tera last updated on 23/May/15

jika α dan β adalah akar−akar  persamaan x^2 +x+1=0 maka   nilai α^(2013) +β^(2301) =.....  a.−2   c.0    e.2    b.−1   d.1

Answered by prakash jain last updated on 23/May/15

Root of equation are ω and ω^2   where 1, ω, ω^2  are cube root of unity.  ω^(2013) +(ω^2 )^(2301) =(ω^3 )^(671) +(ω^3 )^(2×767) =1+1=2

Commented byprakash jain last updated on 23/May/15

Cube root of 1 are solutions of equation  x^3 =1  x^3 −1=0  (x−1)(1+x+x^2 )=0  1+x+x^2  gives two solutions ω and ω^2   1−x gives one solution 1  The three solution are 1, w, w^2