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

1 Answer
JMicheli
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.

Related questions
See all questions in Radical Equations
Impact of this question
2073 views around the world
You can reuse this answer
Creative Commons License