Could anyone explain this problem to me? If x is a positive real number and x^2 + 1/(x^2) = 3, then x^3 + 1/(x^3) = ? Thanks in advance!

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- February 5th 2011, 02:52 PMeric1299171Math Contest Problem
Could anyone explain this problem to me? If x is a positive real number and x^2 + 1/(x^2) = 3, then x^3 + 1/(x^3) = ? Thanks in advance!

- February 5th 2011, 02:54 PMdwsmith
- February 5th 2011, 02:57 PMeric1299171
It's a problem from the 2007 Luzerne County Math Contest.

- February 5th 2011, 03:01 PMdwsmith
- February 5th 2011, 03:11 PMeric1299171
If you use the quadratic formula, wouldn't you get a 5 under the square root instead of a -7?

- February 5th 2011, 03:13 PMdwsmith
- February 5th 2011, 03:18 PMeric1299171
Thanks. =) Then after you solve for x how do you figure out what x^3 + 1/(x^3) is? I tried plugging back in but it turned really ugly.

- February 5th 2011, 05:33 PMLoblawsLawBlog
You can do it without explicitly solving for . We have

. Since is positive, .

Now expand . - February 5th 2011, 07:40 PMeric1299171
Thank you so much! My math teacher and I were working on this for hours. =)