We immediately find that
are possible choices, which makes
, respectively.
If
, we can eliminate the factor of
to get
Note that if
, we have equality, but this goes against our assumption that
. Note that
for all
, which means
is a monotonically increasing function, and is bounded between -1 and 1. On the other hand,
is a monotonically decreasing function that is unbounded. From this you can gather that the two functions never intersect for
(since
is always negative while
is always positive), which means
is the only solution to the equation above. However, this solution is actually extraneous, since the original equation contains a factor of
. So, in fact, the equation above has no solution for
.
That leaves us with
,
, and
.