1960 IMO Problems/Problem 2
Contents
[hide]Problem
For what values of the variable does the following inequality hold:
Solution
Set , where .
After simplifying, we get
So
Which gives and hence .
But makes the LHS indeterminate.
So, answer: , except .
Solution 2
If , then the LHS is defined and rewrites as follows:
The inequality therefore holds if and only if or
So and therefore . But if then the inequality makes no sense, since is imaginary. So the original inequality holds iff is in
See Also
1960 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |