SOLUTION: 5) For the equation x-sqrt x=0, and perform the following: a) Solve for all values of x that satisfies the equation. Answer: Show work in this space b) Graph the

Algebra ->  Square-cubic-other-roots -> SOLUTION: 5) For the equation x-sqrt x=0, and perform the following: a) Solve for all values of x that satisfies the equation. Answer: Show work in this space b) Graph the      Log On


   

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:
Show work in this space



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
c) How does the graph relate to part a?
Answer:

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
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%28x%29=0
x-sqrt%28x%29%2Bsqrt%28x%29=0%2Bsqrt%28x%29
x=sqrt%28x%29
%28x%29%5E2=%28sqrt%28x%29%29%5E2
x%5E2=x
x%5E2-x=x-x
x%5E2-x=0
x%28x-1%29=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
%280%29-sqrt%280%29=0
0-0=0 True, x=0 is valid
for x=1
%281%29-sqrt%281%29=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%28300%2C200%2C-3%2C5%2C-3%2C5%2Cx%2Csqrt%28x%29%29
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!!!!