Question

How do you solve `3+sqrt[x]=sqrt[x-3]` and find any extraneous solutions?

Answer 1

No feasible solution.

Explanation:

The feasible solutions are for `x ge 0` and `x-3 ge 0` or resuming `x ge 3`

Now

`3=sqrt(x-3)-sqrtx=sqrt x(sqrt(1-3/x)-1)` but with `x ge 3`

`sqrt(1-3/x)-1 < 0` so no solution for this equation