Question 36
Let $a,b,c$ be positive real numbers satisfying $\min\{a+b,b+c,c+a\}\gt \sqrt2$ and $a^2+b^2+c^2=3$. Prove
$$\frac{a}{(b+c-a)^2}+\frac{b}{(c+a-b)^2}+\frac{c}{(a+b-c)^2}\ge\frac3{(abc)^2}.$$
$$\frac{a}{(b+c-a)^2}+\frac{b}{(c+a-b)^2}+\frac{c}{(a+b-c)^2}\ge\frac3{(abc)^2}.$$