How to prove that for all $a,b,c$ whuch are the side lengths of triangles, $\sum_{cyc} \frac{4c^2+a^2+b^2}{b^2+c^2} \leq 9$?

by Sushil basak   Last Updated October 09, 2019 15:20 PM - source

How to prove that for all $a,b,c$ which are the side lengths of triangles, $\sum_{cyc} \frac{4c^2+a^2+b^2}{b^2+c^2} \leq 9$?

I tried using Jensen, but the differential is so long. I cannot think of any other method to kill it.



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