MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Purple Comet Problems
2003 Purple Comet Problems
15
15
Part of
2003 Purple Comet Problems
Problems
(1)
Problem 15, Fall 2003 , MS and HS
Source:
6/23/2011
Let
r
r
r
be a real number such that
r
3
−
1
r
3
=
2
\sqrt[3]{r} - \frac{1}{\sqrt[3]{r}}=2
3
r
−
3
r
1
=
2
. Find
r
3
−
1
r
3
r^3 - \frac{1}{r^3}
r
3
−
r
3
1
.