Posted by **JESSICA** on Monday, October 15, 2007 at 9:31pm.

I got this problem but its unrelated to any material that we worked on. Can some please help me to solve it and please explain it. Thanks

Problem states:

Given:

x+(1/x)= square root of 3

PROVE:

(x^13)+(1/(x^13))= square root of 3

- CALCULUS -
**Count Iblis**, Monday, October 15, 2007 at 9:53pm
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)

- CALCULUS -
**bobpursley**, Monday, October 15, 2007 at 10:00pm
solve for x in the given equation using the quadratic equation. Then, describe it on the complex plane, a vector at 60deg.

But x^13 is the same value, rotated around the plane twice. 13*60=60 +n360

QED

## Answer This Question

## Related Questions

- Algebra - Use the quadratic formula to solve the equation. Give exact answers: ...
- Pre Algebra - Please help me with some problems. Thank you! Solve the equation ...
- College Algebra help please - I need some help with a handful of questions. I ...
- Calculus - A rectangle is bounded by the x axis and the semicircle = square root...
- alg.2 - Solve for x... square root x+16=2+square root x+4. I tried doing this ...
- College Algebra - I need some help with a handful of questions. I need to see ...
- College Algebra - I need some help with a handful of questions. I need to see ...
- Algebra - I have some problems that I am having trouble with and I have some ...
- Math - Multiply 3^to the square root of 2* 3^the square root of 4. I got 3^to ...
- Algebra 2 - could you walk me thorugh these problems simplfy square root 18 - 3 ...

More Related Questions