Thanks for feedback.
However, it gets rather messy rather quickly.
First case
(a):
and
(b):
(a) is easy, we get
(b) is not so easy, we don't know the sign of .
If then the RHS , so for we must study the sign of the LHS . On the other hand, the LHS is always positive and we must study the sign of the RHS.
: (LHS)R must reach a minimum value before LHS can be positive. That value is
.
For
we have
which is negative.
So for
we can't met equality[/TEX].
For
if
then
if
then
Then
For
which is negative
So for
we require
.
For
which is positive
For
we require
: (RHS)When
the RHS is always negative.
For
we have
if
then
if
then
Then
For
which is positive
For
which is negative
For
we have
which is negative
We therefore conclude
For we require
For we require
For we require .
Second case
(a):
and
(b):
(a) is easy, we get
(b)
: (LHS)R must reach a minimum value before LHS can be positive. That value is
.
For
we have
which is negative.
So for
we require
.
For
if
then
if
then
Then
For
which is negative
For
which is positive
For
we can't meet equality.
For
we require
: (RHS)When
the RHS is always negative.
For
we have
if
then
if
then
Then
For
which is positive
For
which is negative
For
we have
which is negative
We therefore conclude
For we can't meet inequality
For we require
For we require .
For the other inequality