SOLUTION: 1. Is √x ^2 = x an identity (true for all values of x)? Explain the answer 2. For the equation x - √x = 0 perform the following a. Solve for all val

Algebra ->  College  -> Linear Algebra -> SOLUTION: 1. Is √x ^2 = x an identity (true for all values of x)? Explain the answer 2. For the equation x - √x = 0 perform the following a. Solve for all val      Log On


   

Question 24998: 1. Is √x ^2 = x an identity (true for all values of x)?
Explain the answer
2. For the equation x - √x = 0 perform the following
a. Solve for all values of x that satisfies the equation.
b. graph the functions y = x and y = √ x on the same graph (by plotting points)

How does the graph relate to part a?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1. No, sqrt[(-3)^2] is not -3
2. a. x-sqrt(x) =0
x = sqrt (x)
Square both sides to get:
x^2 = x
x^2-x=0
x(x-1)=0
x =0 or x=1
b. That's a good way to solve an equation. Graph the
left side of the equation, i.e. y=x and the right side
y=sqrtx and see where they intersect. The x-value of the
points of intersection will be the potential answers to
the problem. It is possible that a particular answer
will be extraneous so potential answers need to be checked
in the original equation.
Cheers,
Stan H.