Assuming a and b are positive numbers, then
for the first inequality:
.
,
Both sides times , gives the first inequality.
for the second inequality:
.
Both sides divided by gives the second inequality.
Left inequality...
We know from the right inequality that
Hence
We are now asking if
No..
inconclusive
We can say...
by 2 times the amount that
We can examine the case for
Difference is
the ratio is
Since...
then....
The ratio is ,
therefore by a margin not greater than
the difference between and