Question 32714
Put values of x=0,-1,1,-2,2,and so on for both functions. Plot the corresponding results.
Your graph should look like this:
{{{ graph( 600, 600, -10, 10, -10, 10, x, sqrt(x) ) }}}
You can see the point of intersection of these graphs clearly.
To solve this using algaebra,
y=x....[1]
y=sqrt(x)....[2]
solve the two simueltanously,
{{{x=sqrt(x)}}}
{{{x-sqrt(x)=0}}}
{{{sqrt(x)(sqrt(x)-1)=0}}}
This implies
sqrt(x)=0 and (sqrt(x)-1)=0
sqrt(x)=0 and sqrt(x)=1
so the only places where this condition for the number and its root to be the same will be fulfilled will be at 0 and 1
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Hope this helps,
xC