Find the largest $C \in \mathbb{R}$ such that \[\frac{x+z}{(x-z)^2} +\frac{x+w}{(x-w)^2} +\frac{y+z}{(y-z)^2}+\frac{y+w}{(y-w)^2} + \sum_{cyc} \frac{1}{x} \ge \frac{C}{x+y+z+w}\] where $x,y,z,w \in \mathbb{R^+}$. Author: Hunter Spink
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Tags: inequalities proposed, inequalities
Find the largest $C \in \mathbb{R}$ such that \[\frac{x+z}{(x-z)^2} +\frac{x+w}{(x-w)^2} +\frac{y+z}{(y-z)^2}+\frac{y+w}{(y-w)^2} + \sum_{cyc} \frac{1}{x} \ge \frac{C}{x+y+z+w}\] where $x,y,z,w \in \mathbb{R^+}$. Author: Hunter Spink