matinyousefi wrote: Find the greatest possible value of $s>0$, such that for any positive real numbers $a,b,c$, $$(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a})^2 \geq s(\frac{1}{a^2+bc}+\frac{1}{b^2+ca}+\frac{1}{c^2+ab}).$$ For $b=c=1$ and $a\rightarrow+\infty$ we obtain $s\leq1$, but for $s=1$ the inequality is obviously true after full expanding.