1972 IMO Problems/Problem 4
Find all solutions of the system of inequalities where are positive real numbers.
Solution
Add the five equations together to get
Expanding and combining, we get
Every term is , so every term must .
From the first term, we can deduce that . From the second term, . From the third term, . From the fourth term, .
Therefore, is the only solution.
Borrowed from [1]
See Also
1972 IMO (Problems) • Resources | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |