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avatar+93 

If \(\left( r + \frac{1}{r} \right)^2 = 3,\) then find \(r^3 + \frac{1}{r^3}.\)

 May 17, 2019
 #1
avatar+4287 
+2

These problems are actually fun to work with it once you get used to them :).

 

If you know this...\(r+\frac{1}{r}\cdot[(r+\frac{1}{r})^2-3]=r^3+\frac{1}{r^3}.\)

 

Plugging the value of \(({r}+\frac{1}{r})^2\) in, we get \(r+\frac{1}{r}\cdot0=r^3+\frac{1}{r^3}.\) and thus the answer is \(\boxed{0}.\)

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 May 17, 2019
 #2
avatar+93 
+1

thanks I understand

 May 20, 2019

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