Prove that
\frac{1}{a^{2}+2}+\frac{1}{b^{2}+2}+\frac{1}{c^{2}+2} \leq \frac{1}{6 a b+c^{2}}+\frac{1}{6 b c+a^{2}}+\frac{1}{6 c a+b^{2}}
for any positive real numbers a, b and c satisfying a^{2}+b^{2}+c^{2}=1.
Prove that
for any positive real numbers a, b and c satisfying a^{2}+b^{2}+c^{2}=1.