1964 IMO Problems/Problem 2
Suppose are the sides of a triangle. Prove that
Let , , and . Then, , , and . By AM-GM,
Multiplying these equations, we have We can now simplify: ~mathboy100
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.
Rearrange to get which is true by Schur's inequality.
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