Question 30
Show that for all positive numbers $a$, $b$ and $c$ the following inequality holds:
$$
\frac{(a+b-c)^2}{c} + \frac{(b+c-a)^2}{a} + \frac{(c+a-b)^2}{b} \geq 6.
$$
When does the equality hold?
$$
\frac{(a+b-c)^2}{c} + \frac{(b+c-a)^2}{a} + \frac{(c+a-b)^2}{b} \geq 6.
$$
When does the equality hold?