Sean $a,b,c>0.$ Demuestre que $\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a} \ge \frac{1}{\sqrt{2a^2+2bc}}+\frac{1}{\sqrt{2b^2+2ca}}+\frac{1}{\sqrt{2c^2+2ab}}$ Dr.frankenstein