3 replies to this topic

[DOTOANNANG]

$a\,,b\,,c> 0$

 

$$\frac{a}{\sqrt{a+ b}}+ \frac{b}{\sqrt{b+ c}}+ \frac{c}{\sqrt{c+ a}}\leqq \frac{5}{4}\,\sqrt{a+ b+ c}$$

Edited by DOTOANNANG, 26-04-2018 - 09:56.

[DOTOANNANG]

$a\,,b\,,c\,,d> 0$

 

$$\frac{a}{\sqrt{a+ b}}+ \frac{b}{\sqrt{b+ c}}+ \frac{c}{\sqrt{c+ d}}+ \frac{d}{\sqrt{d+ a}}\leqq \frac{\sqrt{33}}{4}\,\sqrt{a+ b+ c+ d}$$

[tr2512]

$a\,,b\,,c\,,d> 0$

 

$$\frac{a}{\sqrt{a+ b}}+ \frac{b}{\sqrt{b+ c}}+ \frac{c}{\sqrt{c+ d}}+ \frac{d}{\sqrt{d+ a}}\leqq \frac{\sqrt{33}}{4}\,\sqrt{a+ b+ c+ d}$$

Ủa, e nhớ bài này hệ số tốt nhất nó xấu lắm cơ mà nhỉ bài này chắc không có dấu bằng  

[DOTOANNANG]

$a\,,b\,,c> 0$

 

$$\frac{a}{\sqrt{a+ b}}+ \frac{b}{\sqrt{b+ c}}+ \frac{c}{\sqrt{c+ a}}\leqq \frac{5}{4}\,\sqrt{a+ b+ c}$$

 

$$\sum\limits_{cyc} \frac{a}{\sqrt{a+ b}}\leqq \frac{5}{4}\sqrt{\left ( a+ b+ c \right )\left [ 1- \frac{8\prod\limits_{cyc}a }{25\prod\limits_{cyc}\left ( a+ b \right )} \right ]}$$