2003 Indonesia MO Problems/Problem 5
Problem
For every real number , prove the following inequality
and determine when the equality holds.
Solution
By the Trivial Inequality,
and
Adding all the equations, expanding the terms, and rearranging the resulting terms results in
Equality holds when
When that happens,
so
See Also
2003 Indonesia MO (Problems) | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Problem 6 |
All Indonesia MO Problems and Solutions |