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Question Number 155069 by mathdanisur last updated on 24/Sep/21

$$\mathrm{if}\mathrm{x};\mathrm{y};\mathrm{z}>0\mathrm{such}\mathrm{that}\mathrm{x}+\mathrm{y}+\mathrm{z}=3$$ $$\mathrm{and}0⩽\mathit{\lambda }⩽1\mathrm{then}\mathrm{prove}\mathrm{that}:$$ $$\frac{\mathrm{x}}{{\mathrm{y}}^2+\lambda }+\frac{\mathrm{y}}{{\mathrm{z}}^2+\lambda }+\frac{\mathrm{z}}{{\mathrm{x}}^2+\lambda }⩾\frac{3}{\lambda +1}$$

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