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

Jul 28, 2016

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.