Example 4.1.4
Solve the equation
in
.
Let
, where
are real numbers. We have:
As
, for any
, we have
, i.e.
. We consider now two cases:
- (i)
- If
, with
, we have
. The first equation has one solution,
given by
.
- (ii)
- If
, with
, we have
. The first equation implies now that
, and has no solution.
We conclude: the solution set of the given equation in
is
.
Example 4.1.5
Solve the equation
in
.
Let
, where
are real numbers. We have:
As
, for any
, we have
, i.e.
. We consider now two cases:
- (i)
- If
, for
, we have
. The second equation implies
, i.e.
.
- (ii)
- If
, for
, we have
.The second equation implies
,which has no real solution.
We conclude: the solution set of the given equation in
is
.