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