cho $a,b,c>0$ .CMR:
$ \frac{a}{\sqrt{2a+b}} +\frac{b}{\sqrt{2b+c}} +\frac{c}{\sqrt{2c+a}} \leq \sqrt{a+b+c}$
Ta có : P=$\frac{a}{\sqrt{2a+b}}\leq \sqrt{(\sum a)(\sum \frac{a}{2a+b})}=\sqrt{(\sum a)\frac{1}{2}(3-\sum \frac{b}{2a+b})}= \sqrt{(\sum a)\frac{1}{2}(3-\sum \frac{b^{2}}{2ab+b^{2}})}\leq \sqrt{(\sum a)\frac{1}{2}(3-\frac{(\sum a)^{2}}{(\sum a)^{2}})}=\sqrt{\sum a}$(đpcm)