



Now if

, then both

and

. Adding two positive numbers gives another positive number, so

. Why this is useful will be apparent shortly.
Back to the identity:

Factorizing the left hand side, we have

Now, any number squared will be positive, which means the right hand side is necessarily greater than 0.
We showed earlier that

. So we understand that we have

The only way to multiply a number by a positive number to get yet another positive number is to have the first number also be positive, which means

and from this it follows that

in the provided region.