Question 56676
For the equation {{{x-2*sqrt(x)=0}}} , perform the following:
a) 	Solve for all values of x that satisfies the equation.
Answer:  x={0,4}
Show work in this space.
{{{x-2*sqrt(x)=0}}}
{{{x-2*sqrt(x)+2*sqrt(x)=0+2*sqrt(x)}}}
{{{x=2*sqrt(x)}}}
{{{x^2=(2*sqrt(x))^2}}}
{{{x^2=4x}}}
{{{x^2-4x=4x-4x}}}
{{{x^2-4x=0}}}
{{{x(x-4)=0}}}
{{{x=0}}} and {{{x-4=0}}}-->{{{x=4}}}
Check for extraneous solutions:
{{{(0)-2*sqrt(0)=0}}}
{{{0-0=0}}}
{{{0=0}}} x=0 checks.
{{{(4)-2*sqrt(4)=0}}}
{{{4-2(2)=0}}}
{{{4-4=0}}}
{{{0=0}}} x=4 checks also.
 
b) 	Graph the functions y = x and {{{y=2sqrt(x)}}}  on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
Graph:
 
Points of intersection: (0,0) and (4,4)  
For y=x
Let x=0, solve for y
y=0, plot (0,0)
Let x=4, solve for y
y=4, plot (4,4)
Connect the dots and you have a line.
For {{{y=2*sqrt(x)}}}
Let x=0
{{{y=2*sqrt(0)}}}
{{{y=2(0)}}}
y=0, Plot (0,0)
Let x=1
{{{y=2*sqrt(1)}}}
{{{y=2(1)}}}
{{{y=2}}}, plot (1,2)
Let x=4
{{{y=2*sqrt(4)}}}
{{{y=2*2}}}
y=4, plot (4,4)
Connect the dots and you have a curve.
Their points of intersections are (0,0) and (4,4)
{{{graph(300,200,-10,10,-10,10,x,2*sqrt(x))}}}
Happy Calculating!!!!