11. Let $a b c$ and $d$ be four distinct positive real numbers that satisfy the equations
$$
\left(a^{2012}-c^{2012}\right)\left(a^{2012}-d^{2012}\right)=2011
$$
and
$$
\left(b^{2012}-c^{2012}\right)\left(b^{2012}-d^{2012}\right)=2011
$$

Find the value of $(c d)^{2012}-(a b)^{2012}$.
11. Answer: 2011
Let $A=a^{2012}, B=b^{2012}, C=c^{2012}$ and $D=d^{2012}$. Then $A$ and $B$ are distinct roots of the equation $(x-C)(x-D)=2011$. Thus the product of roots, $A B=C D-2011$ and $C D-A B=2011$.