Question 72920
5) 	For the equation x-sqrt x=0, and perform the following:
a) 	Solve for all values of x that satisfies the equation.
Answer: 
x=0 or x=1
:
Show work in this space	
{{{x-sqrt(x)=0}}}
{{{x-sqrt(x)+sqrt(x)=0+sqrt(x)}}}
{{{x=sqrt(x)}}}
{{{(x)^2=(sqrt(x))^2}}}
{{{x^2=x}}}
{{{x^2-x=x-x}}}
{{{x^2-x=0}}}
{{{x(x-1)=0}}}
x=0 or x-1=0
x=0 or x-1+1=0+1
x=0 or x=1
Check for extraneous solutions:
for x=0
{{{(0)-sqrt(0)=0}}}
{{{0-0=0}}} True, x=0 is valid
for x=1
{{{(1)-sqrt(1)=0}}}
{{{1-1=0}}} True, x=1 is valid.
:


b) 	Graph the functions y=x, and y=sqrt x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

Graph 
{{{graph(300,200,-3,5,-3,5,x,sqrt(x))}}}
They intersect at (0,0) and (1,1)
:
c) 	How does the graph relate to part a?
Answer: 
The x values of their points of intersection are the solutions to the equation in question.
:
Happy Calculating!!!!