Question 7
Let $a, b$, and $c$ be positive real numbers satisfying $\min (a+b, b+c, c+a)\gt \sqrt{2}$ and $a^{2}+b^{2}+c^{2}=3$. Prove that
$$
\frac{a}{(b+c-a)^{2}}+\frac{b}{(c+a-b)^{2}}+\frac{c}{(a+b-c)^{2}} \geq \frac{3}{(a b c)^{2}}
$$
$$
\frac{a}{(b+c-a)^{2}}+\frac{b}{(c+a-b)^{2}}+\frac{c}{(a+b-c)^{2}} \geq \frac{3}{(a b c)^{2}}
$$