[Toán 9] C/M BĐT

E

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Từ GT \Rightarrow $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{ab}+\dfrac{1}{bc}+\dfrac{1}{ac}=6$
AD AM-GM:
$\dfrac{1}{{a^2}}+1 \ge \dfrac{2}{a}$
$\dfrac{1}{{b^2}}+1 \ge \dfrac{2}{b}$
$\dfrac{1}{{c^2}}+1 \ge \dfrac{2}{c}$

$\dfrac{1}{{a^2}}+\dfrac{1}{{b^2}} \ge \dfrac{2}{ab}$
$\dfrac{1}{{b^2}}+\dfrac{1}{{c^2}} \ge \dfrac{2}{bc}$
$\dfrac{1}{{c^2}}+\dfrac{1}{{a^2}} \ge \dfrac{2}{ac}$

Cộng theo vế \Rightarrow đpcm
 
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