Inequality

[choisiwon]

for a, b, c are three positive numbers. Prove that:
[tex]\frac{a^{2}}{a+b}+\frac{b^{2}}{b+c}+\frac{c^{2}}{c+a}[/tex][tex]\geq \frac{\sqrt{2}}{4}\left(\sqrt{a^{2}+b^{2}} +\sqrt{b^{2}+c^{2}}+\sqrt{c^{2}+a^{2}}\right)[/tex].

[puzzled by equation]

I tried to solve the equation but unsuccessfully although I thought 1.5 hours.
Can you give me any instructions, please?