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nmtuan2001

nmtuan2001

Đăng ký: 03-07-2014
Offline Đăng nhập: 14-04-2019 - 18:39
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$\sqrt[3]{\frac{2a}{4a+4b+c}}+\sqrt[3...

14-03-2018 - 21:17

Cho $a,b,c>0$. Chứng minh
$$\sqrt[3]{\frac{2a}{4a+4b+c}}+\sqrt[3]{\frac{2b}{4b+4c+a}}+\sqrt[3]{\frac{2c}{4c+4a+b}}<2$$
(Nguồn: Tạp chí Crux 2011)
Ps: BĐT khá lỏng nhưng có cách giải khá hay

$\frac{a}{b}+\frac{b}{c}+\f...

23-02-2015 - 20:04

Cho $a,b,c>0$. CMR: $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq \frac{9(a^2+b^2+c^2)}{(a+b+c)^2}$.

(Chặt hơn BĐT $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq \frac{3 \sqrt{3(a^2+b^2+c^2)}}{a+b+c}$)


$\frac{a}{b}+\frac{b}{c}+\f...

23-02-2015 - 20:02

Cho $a,b,c>0$. CMR: $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geq \frac{3 \sqrt{3(a^2+b^2+c^2)}}{a+b+c}$


$3(a^2b^2+b^2c^2+c^2a^2)(a^2+b^2+c^2) \geq (a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^...

16-12-2014 - 06:42

Cho $a,b,c>0$. CMR: $3(a^2b^2+b^2c^2+c^2a^2)(a^2+b^2+c^2) \geq (a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^2)$

(Nguồn: Mathematical Reflection)


$\frac{a^2}{b(b+c)}+\frac{b^2}{c(c+a)...

13-12-2014 - 22:54

Cho $a,b,c>0$. CMR:$\frac{a^2}{b(b+c)}+\frac{b^2}{c(c+a)}+\frac{c^2}{a(a+b)} \geq \frac{3}{2}$