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

FlyEaglesFly May 17, 2019

#1**+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 \(\boxed{0}.\)

.tertre May 17, 2019