Asked by Leslie
Given:
x+(1/x)= square root of 3
PROVE:
(x^13)+(1/(x^13))= square root of 3
x+(1/x)= square root of 3
PROVE:
(x^13)+(1/(x^13))= square root of 3
Answers
Answered by
Count Iblis
Put x = exp(i t)
Then:
x + 1/x = 2 cos(t)
x + 1/x = sqrt(3) ---->
cos(t) = sqrt(3)/2 ---->
t = ±pi/6 (adding a multiple of 2 pi leaves x invariant)
x^(13) + x^(-13) = 2 cos(13 t) =
2 cos(13/6 pi) = 2 cos(pi/6) = sqrt(3)
Then:
x + 1/x = 2 cos(t)
x + 1/x = sqrt(3) ---->
cos(t) = sqrt(3)/2 ---->
t = ±pi/6 (adding a multiple of 2 pi leaves x invariant)
x^(13) + x^(-13) = 2 cos(13 t) =
2 cos(13/6 pi) = 2 cos(pi/6) = sqrt(3)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.