1990 AIME Problems/Problem 2
Problem
Find the value of .
Solution
Suppose that is in the form of . FOILing yields that . This implies that and equal one of . The possible sets are and ; the latter can be discarded since the square root must be positive. This means that . Repeating this for , the only feasible possibility is .
Rewriting, we get . Using the difference of cubes, we get that .
See also
1990 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |