How do you solve # sqrt[x-5]-sqrt[x-3]=4# and find any extraneous solutions?
If you multiply both sides by the conjugate,
Please observe that the left side simplifies to a negative number:
Divide both sides by 4 and flip the equation:
This means that no solution exists.
Think of it this way.
You are starting with
(which must be a positive number) and you are subtracting another positive number
and you obtain a positive number
but, if you add the two numbers, you obtain a negative number, -1/2?