A Variable and Its Reciprocal, Each Cubed

Date: 11/20/2010 at 12:18:23
From: AYUSH
Subject: IDENTITY

If x + 1/x = r^3, then what does this equal?

   xxx + (1/xxx)

Date: 11/22/2010 at 12:34:14
From: Doctor Ali
Subject: Re: IDENTITY

Hi Ayush!

Thanks for writing to Dr. Math.

Assume that we know a simpler version of what you are given:

   x + 1/x = A

Now, in order to find A^2, we just need to raise both sides of the
equation to the second power. That is,

   (x + 1/x)^2 = x^2 + 1/x^2 + 2 x/x = A^2

So,

   x^2 + 1/x^2 = A^2 - 2

Does that make sense?

Can you use the same method to find x^3 + 1/x^3?

Please write back if you still have any difficulties.

- Doctor Ali, The Math Forum
  http://mathforum.org/dr.math/