
Prove:
We will proceed as follows:
For all ,
.
That is,
When
we have
It means
We also have
As a result, (1) becomes
Rewrite it as
where denotes
, we see that
is a positive root of
Clearly,
is also a positive root of
since
Moreover (see Exercise 1),
has only one positive root
Therefore, it must be true that

Exercise-1 Prove: has only one positive root.
Exercise-2 Prove: