[math]\frac{b+c}{\sqrt{a}} + \frac{c + a}{\sqrt{b}} + \frac{a + b}{\sqrt{c}} \geq 2(\sqrt{\dfrac{bc}{a}}+\sqrt{\dfrac{ca}{b}}+\sqrt{\dfrac{ab}{c}}) = (\sqrt{\dfrac{ca}{b}}+\sqrt{\dfrac{ab}{c}})+(\sqrt{\dfrac{ab}{c}}+\sqrt{\dfrac{bc}{a}})+(\sqrt{\dfrac{bc}{a}}+\sqrt{\dfrac{ca}{b}}) [/math][math]\geq 2(\sqrt{a}+\sqrt{b}+\sqrt{c}) \geq \sqrt{a}+\sqrt{b}+\sqrt{c}+3\sqrt[6]{abc}=\sqrt{a}+\sqrt{b}+\sqrt{c}+3[/math]