1973 IMO Problems/Problem 3
Problem
Let and be real numbers for which the equation has at least one real solution. For all such pairs , find the minimum value of .
Solution
Substitute to change the original equation into . This equation has solutions . We also know that . So,
Rearranging and squaring both sides,
So, .
Therefore, the smallest possible value of is , when and .
Borrowed from [1]
See Also
1973 IMO (Problems) • Resources | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
All IMO Problems and Solutions |