The right-hand side could not be simplified like the left-hand side. To continue the simplification, we would have to expand the parentheses on the right-hand side.
The analytical approach didn't eliminate the radical. Therefore, this is not a good way of solving this equation.
Numerical approach
A numerical approach is basically trial-and-error. By substituting appropriate values of x in the equation, we can find an approximate or exact solution. However, to use this approach, we must have some basic idea of what the solution might be. Let's show an example.
sqrt(x)=12
We know that sqrt(9)=3 and sqrt(16)=4, so the solution to the radical equation is between 3 and 4. However, for the given equation, there is no real clue as to where the solution might be. Therefore, this is not a good way of solving the equation.
Graphical approach
To solve a radical equation graphically, we draw the left-hand side and right-hand side of the equation as individual graphs.
f(x)= sqrt(x+3)-sqrt(x-2) and g(x)= 1
By identifying the x-value where these graphs intersect, we can solve the equation.
The solution is x=6. As we can see, the graphical approach is preferred in this instance.
