1979 IMO Problems/Problem 5
Problem
Determine all real numbers a for which there exists non-negative reals which satisfy the relations
Solution
Let , and . For all pairs , letThen we have on one handTherefore \(1)and on the other hand \ (2)Then from (1) we haveand from (2)so Besides we also have from (1)and from (2)and for where in the right hand we have that, so,and, sofor From the latter and (2) we also haveSo we have that If , take , for . Then , , and
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 |