ELMO SL 2011 A5

Given positive reals $x,y,z$ such that $xy+yz+zx=1$ , show that $\sum_{\text{cyc}}\sqrt{(xy+kx+ky)(xz+kx+kz)}\ge k^2,$ where $k=2+\sqrt{3}$ .

Victor Wang.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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