56. Determine the largest real number $C$, for all real numbers $x, y, x \neq y$, and $xy=2$, such that the inequality $\frac{\left[(x+y)^{2}-6\right]\left[(x-y)^{2}+8\right]}{(x-y)^{2}} \geqslant C$ holds. (2002 Austrian Mathematical Olympiad Problem)
$\begin{array}{l}\text { 56. Since } \frac{\left[(x+y)^{2}-6\right]\left[(x-y)^{2}+8\right]}{(x-y)^{2}}=\frac{\left[(x-y)^{2}+4 x y-6\right]\left[(x-y)^{2}+8\right]}{(x-y)^{2}}= \\ \frac{\left[(x-y)^{2}+2\right]\left[(x-y)^{2}+8\right]}{(x-y)^{2}}=(x-y)^{2}+\frac{16}{(x-y)^{2}}+10 \geqslant 18 \text {, therefore } C_{\text {max }}=18 \text {, with equality } \\ \text { if and only if }(x-y)^{2}=4 \text {, and } x y=2 \text {, i.e., when } x-y= \pm 2 \text {, and } x y=2 \text {, equality holds. }\end{array}$