# How do you solve # sqrt[x-5]-sqrt[x-3]=4# and find any extraneous solutions?

##### 1 Answer

Aug 31, 2017

GIven:

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

4

but, if you add the two numbers, you obtain a negative number, -1/2?

No.