Chủ đề này có 1 trả lời

[Nguyen Duc Thuan]

Cho $a\geq b\geq c>0$. CMR:

 

$\frac{a^2-4b^2}{c}+\frac{9c^2-4b^2}{a}+\frac{a^2-9c^2}{b}\geq 7a-16b+3c$

[4869msnssk]

Cho $a\geq b\geq c>0$. CMR:

 

$\frac{a^2-4b^2}{c}+\frac{9c^2-4b^2}{a}+\frac{a^2-9c^2}{b}\geq 7a-16b+3c$

$(a+2b)\geq 3c\Rightarrow \frac{a^{2}-4b^{2}}{c}\geq 3(a-2b)=3a-6b$

$(3c+2b)\leq 5a\Rightarrow \frac{9c^{2}-4b^{2}}{a}\geq 5(3c-2b)=15c-10b$

$(a+3c)>b\Rightarrow \frac{a^{2}-9c^{2}}{b}\geq (a-3c)$