Question

How do you solve `sqrt(x-3)-sqrtx=3`?

Answer 1

There are no solutions.

Explanation:

The equation given can be reformed to give:
`sqrt(x-3) = sqrt(x)+3`

This is equivalent to asking where two functions intersect. The functions in this case are:
`y = sqrt(x-3)`
`y = sqrt(x) + 3`

Merely observing the graph of the functions makes it clear that the two will never intersect:
graph{(y-sqrt(x-3))(y-sqrt(x)+3)=0 [-10.97, 46.77, -9.94, 18.93]}

You may note that the functions appear to head toward one another at `x=0`. At this point the functions both become imaginary valued. If the graph were continued in complex space, they still would not intersect.