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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Originally Posted by eric1299171 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! A contest you are doing now or an old problem?
It's a problem from the 2007 Luzerne County Math Contest.
Originally Posted by eric1299171 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!
Last edited by dwsmith; February 5th 2011 at 04:13 PM. Reason: forgot to square the -3
If you use the quadratic formula, wouldn't you get a 5 under the square root instead of a -7?
Originally Posted by eric1299171 If you use the quadratic formula, wouldn't you get a 5 under the square root instead of a -7? Correct, I forgot to square.
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.
You can do it without explicitly solving for . We have . Since is positive, . Now expand .
Thank you so much! My math teacher and I were working on this for hours. =)
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