by sqrtneg1 » Wed Mar 24, 2010 1:32 pm
The second equation tells us that [unparseable or potentially dangerous latex formula]. Thus, [unparseable or potentially dangerous latex formula]. This can only be true if [unparseable or potentially dangerous latex formula], and [unparseable or potentially dangerous latex formula]. Substituting those two results into the first equation yields
[unparseable or potentially dangerous latex formula]
Taking advantage of the fact that [unparseable or potentially dangerous latex formula], we find that the smallest possible value of [unparseable or potentially dangerous latex formula] is [unparseable or potentially dangerous latex formula] and the largest is [unparseable or potentially dangerous latex formula], and all numbers in between work.
Thus, the number of possible values of [unparseable or potentially dangerous latex formula] is [unparseable or potentially dangerous latex formula]