Question 77062
<pre><font size = 5><b>
For the equation {{{x - 2*sqrt(x)=0}}} , 
perform the following:
a) Solve for all values of x that 
satisfies the equation. 

{{{x - 2*sqrt(x)=0}}}

Isolate the radical term by adding {{{2*sqrt(x)}}} to both sides

{{{x = 2*sqrt(x)}}} 

Square both sides

{{{x^2 = (2*sqrt(x))^2}}}

{{{x^2 = 4x}}}

Get 0 on the right

{{{x^2 - 4x = 0}}}

Factor x out on the left

{{{x(x-4)=0}}}

Use the zero-factor property
and set each of the factors
x and x-4 equal to 0.

{{{x = 0}}} gives answer as 0
{{{x-4=0}}} gives another answer as 4

We must check these in the original

{{{x - 2*sqrt(x)=0}}}
{{{0 - 2*sqrt(0)=0}}}
{{{0 - 0 = 0}}}
{{{0 = 0}}}
So 0 checks

{{{x - 2*sqrt(x)=0}}}
{{{4 - 2*sqrt(4)=0}}}
{{{4 - 2*2 = 0}}}
{{{4-4=0}}}
(((0=0)))
So 4 checks too.

b) Graph the functions y = x and 
y=2 SQRT of X on the same graph (by plotting 
points if necessary). Show the points of 
intersection of these two graphs.

The idea here is to take the equation
{{{x = 2*sqrt(x)}}} and set y = to each side.
Then graph the two equations. Then the two 
values of y should be equal when the two sides 
of {{{x = 2*sqrt(x)}}} are equal, and that
will be where the graphs intersect.

Some points on {{{y=x}}} are 
(-2,-2), (-1,-1) (2,2) (5,5)

Some points on {{{y=2*sqrt(x)}}} are 
(.5,1.4), (1,2), (3,3.5), (5,4.5)

{{{ graph( 300, 300, -5, 5, -5, 5,0,  x, 2*sqrt(x)) }}}

So we see that the blue curve and the green 
line intersect at (0,0) and (4,4) and the 
x-values are 0 and 4 at those points, which 
correspond to the algebraic solution for x 
above.

Edwin</pre>