Có (\frac{a2}{\sqrt{b+3}}+\frac{b2}{\sqrt{c+3}}+\frac{c2}{\sqrt{a+3}})(\sqrt{b+3}+\sqrt{c+3}+\sqrt{a+3}) \geq (a+b+c)2 (bđt B.C.S)\Rightarrow \frac{a2}{\sqrt{b+3}}+\frac{b2}{\sqrt{c+3}}+\frac{c2}{\sqrt{a+3}} \geq \frac{(a+b+c)2}{\sqrt{b+3}+\sqrt{c+3}+\sqrt{a+3}} \geq \frac{32}{\sqrt{3(a+b+c+9)}} = \frac{3}{2}(đpcm)
Có
$(\frac{a
^2}{\sqrt{b+3}}+\frac{b
^2}{\sqrt{c+3}}+\frac{c
^2}{\sqrt{a+3}})(\sqrt{b+3}+\sqrt{c+3}+\sqrt{a+3}) \geq (a+b+c)
^2
$ (bđt B.C.S)
$\Rightarrow \frac{a
^2}{\sqrt{b+3}}+\frac{b
^2}{\sqrt{c+3}}+\frac{c
^2}{\sqrt{a+3}} \geq \frac{(a+b+c)
^2}{\sqrt{b+3}+\sqrt{c+3}+\sqrt{a+3}} \geq \frac{32}{\sqrt{3(a+b+c+9)}} = \frac{3}{2}
$(đpcm)