A Variable and Its Reciprocal, Each CubedDate: 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/ |
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