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E

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$\dfrac{1}{a+2}=1-\dfrac{1}{b+2}-\dfrac{1}{c+2}=\dfrac{b}{2(b+2)}+\dfrac{c}{2(c+2)} \ge \dfrac{\sqrt{bc}}{\sqrt{(b+2)(c+2)}}$

Tương tự, có:

$\dfrac{1}{b+2} \ge \dfrac{\sqrt{ac}}{\sqrt{(a+2)(c+2)}}$

$\dfrac{1}{c+2} \ge \dfrac{\sqrt{ba}}{\sqrt{(b+2)(a+2)}}$

Nhân theo vế \Rightarrow đpcm
 
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