Tuesday

September 23, 2014

September 23, 2014

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

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 9:53pmPut x = exp(i t)

Then:

x + 1/x = 2 cos(t)

x + 1/x = sqrt(3) ---->

cos(t) = sqrt(3)/2 ---->

t = ąpi/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 10:00pmsolve 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**

Calculus - Hi there I am having some troubles trying to do my calculus homework ...

Math 141 - I am having trouble with this problem. perform the indicated ...

Math subject Calculus - Hi there I am having some difficulties to solve this ...

Calculus - 1/a+1 + 1/a-1 I solved this out by multiplying the (a+1) by (a-1) and...

calculus - I am working on this problem and having some trouble. We're supposed ...

Pre-Calculus - I have to use the substitution method to solve the system of ...

Please Help!!!!!! - Decide whether the following problem can be solved using ...

math - I need some explanation on how to to this problem. (a) 3/3^-4 the answer ...

math - I need some explanation on how to to this problem. (a) 3/3^-4 the answer ...

5th grade math - Which answer shows data with a range of 49? A. 45,69,92,59 B. ...