1964 IMO Problems/Problem 2
Contents
[hide]Problem
Suppose are the sides of a triangle. Prove that
Solution
Let , , and . Then, , , and . By AM-GM,
Multiplying these equations, we have We can now simplify: ~mathboy100
Solution 2
We can use the substitution , , and to get
This is true by AM-GM. We can work backwards to get that the original inequality is true.
eevee9406: This solution uses incorrect reasoning regarding the inequalities.
Solution 3
Rearrange to get which is true by Schur's inequality.
See Also
1964 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |