1979 IMO Problems/Problem 5
Problem
Determine all real numbers a for which there exists positive reals which satisfy the relations
Solution
Discussion thread can be found here: [1]
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See Also
1979 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |
Let , and . For all pairs , let Then we have on one hand Therefore \(1) and on the other hand \ (2) Then from (1) we have and from (2) so Besides we also have from (1) and from (2) and for where in the right hand we have that , so , and , so for From the latter and (2) we also have So we have that
If , take , for . Then , , and