+0

+1
55
2
+93

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

May 17, 2019

#1
+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
+93
+1

thanks I understand

May 20, 2019