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If \(x - \frac{1}{x} = 2\) then find \(x^3 - \frac{1}{x^3}\)

 Jul 12, 2020
 #1
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I can't remember how to solve this problem, but I'm pretty sure the answer is 14.

 Jul 12, 2020
 #2
avatar+732 
+3

Nevermind, I do remember how to solve this. 

 

First let's cube \(x-\frac{1}{x}=2\)

 

\((x-\frac{1}{x})^3=2^3\)

 

\(x^3-3x+\frac{3}{x}-\frac{1}{x^3}=8\)

 

\(x^3-\frac{1}{x^3}=8+3(x-\frac{1}{x})\)

 

\(x^3-\frac{1}{x^3}=8+3(2)\)

 

\(x^3-\frac{1}{x^3}=\boxed{14}\)

 Jul 12, 2020

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