SOLUTION: I am kind of stuck on this problem... maybe someone can assist me! any help would be greatly appreciated! For the equation x - √x = 0, perform the following: a) Solv

Algebra ->  Radicals -> SOLUTION: I am kind of stuck on this problem... maybe someone can assist me! any help would be greatly appreciated! For the equation x - √x = 0, perform the following: a) Solv      Log On


   

Question 72601: I am kind of stuck on this problem... maybe someone can assist me! any help would be greatly appreciated!

For the equation x - √x = 0, 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 = √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:

Found 2 solutions by Edwin McCravy, bucky:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
I am kind of stuck on this problem...
maybe someone can assist me! any help 
would be greatly appreciated! 
                      _
For the equation x - Öx = 0, perform 
the following:
a) Solve for all values of x that satisfies 
the equation.
       _
  x - Öx = 0

Isolate the radical term:
            _
       x = Öx 

Square both sides:

             _
    (x)² = (Öx)² 

      x² = x

Get 0 on the right:

  x² - x = 0

Factor left side

x(x - 1) = 0

Set each factor = 0:

x = 0,  x - 1 = 0
            x = 1

Now we must check these answers in
the original equation:
       _
  x - Öx = 0

Checking x = 0
       _
  0 - Ö0 = 0  
   0 - 0 = 0
       0 = 0

Checking x = 1    
       _
  x - Öx = 0
       _
  1 - Ö1 = 0
   1 - 1 = 0
       0 = 0

b) Graph_the functions y = x and
   y = Öx on the same graph 
(by plotting points if necessary). 

+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+0%2C+x%2C+sqrt%28x%29%29+ 

Show the points of intersection of these two graphs. 

The green line is the graph_of y = x and the blue 
curve is the graph of y = Öx.
They intersect at the two points (0,0) and (1,1).

c) How does the graph relate to part a?

If you wanted to find the points where the green line
crosses the blue curve, you would solve the system:

y = x_
y = Öx

If you subtract the equations you get
         _
0 = x - Öx

 or
     _
x - Öx = 0

which is the original equation
Then you would solve that as above and get
x = 0, x = 1. Then you would substitute
these in one of the equations of the
system above and get y = 0, and y = 1
respectively. So the two points where
the blue curve and and green line intersect
are at (0, 0) and (1, 1).

Edwin

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
First Problem:
.
Solve the equation x+-+sqrt%28x%29+=+0 for all values of x that will satisfy the equation:
.
First add sqrt%28x%29 to both sides of the equation. When you do, the equation becomes:
.
x+=+sqrt%28x%29
.
Next square both sides:
.
x%5E2+=+%28sqrt%28x%29%29%5E2 which becomes x%5E2+=+x
.
Then subtract x from both sides to get:
.
x%5E2+-+x+=+0
.
On the left side factor an x:
.
x%2A%28x-1%29+=+0
.
Note that this equation will be true if either of the factors on the left side equals zero.
This is true because if one of the factors on the left side is zero, the entire left
side will be zero and therefore will equal the right side. So set each of the two factors
equal to zero and you get:
.
x+=+0 and
.
x-1+=0 and by adding 1 to both sides of this equation you get x+=+1.
.
So there are two answers to this equation: x+=+0 and x+=+1. If you substitute
0 for x and if you next substitute 1 for x in the original equation you will see that these
two answers work.
.
Next graph y = x and y = sqrt(x) on the same set of axes:
graph%28800%2C+800%2C-3%2C6%2C-3%2C6%2Cx%2C+sqrt%28x%29%29
.
The green graph represents the y = square root of x and the red graph represents y = x. Note
that the green graph should hit the origin, but there is a flaw in the drafting program that
does not do that. So you will have to make your version of the green graph go down to the
origin.
.
What is the connection where the graphs cross. The crossing points occur at x = 0 and x = 1
which are the answers we got for the problem. At those two points x and the square root of
x are equal so that when you subtract them, the answer is zero.
.
Hope this helps you to understand the problem.