The inequality of the C-S INEQ
Algebra
Level
5
This problem is the proposed problem at 2007 KMO second round for high schoolers.
The answer is 6020.
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1 solution
We shall check the equality. \frac{a}{c+kb}=\frac{b}{a+kc}=\frac{c}{b+ka}=\frac{1}{k+1} so at equality all values are equal to \frac{1}{k+1}. So thereby \frac{1}{2007}={3}{k+1}. Solving we get k=6020