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Question Number 159119 by HongKing last updated on 13/Nov/21

$$\mathrm{Assume}\mathrm{x};\mathrm{y};\mathrm{z}>0\mathrm{and}{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2=12$$ $$\mathrm{Prove}\mathrm{that}:\sum _{\mathbf{cycl}}\frac{\frac{\mathrm{x}}{\mathrm{y}}+1+\frac{\mathrm{y}}{\mathrm{x}}}{\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}}⩽9$$

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