1962 IMO Problems/Problem 4
Problem
Solve the equation .
Solution
First, note that we can write the left hand side as a cubic function of . So there are at most distinct values of that satisfy this equation. Therefore, if we find three values of that satisfy the equation and produce three different , then we found all solutions to this cubic equation (without expanding it, which is another viable option). Indeed, we find that , , and all satisfy the equation, and produce three different values of , namely , , and . So we solve . Therefore, our solutions are:
See Also
1962 IMO (Problems) • Resources) | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |