x- sqrt x=0?

Question

1.) Solve for all values of x that satisfies the equation x- sqrt (x)=0 and show your work.

2.) what are the points of intersection of these two graphs, y=x and y= sqrt (x)

Answer 1

1) x - sqrt(x) = 0

Put sqrt(x) on the right hand side:
x = sqrt(x)

Square both sides:
x² = x

Subtract x from both sides:
x² - x = 0

Factor:
x(x - 1) = 0

So x = 0 or x = 1

2) This is essentially the same question. You would equate the two equations:
y = x
y = sqrt(x)

So:
x = sqrt(x)

Follow the same steps as before:
x² = x
x² - x = 0
x (x - 1) = 0
x = 0 or x = 1

Now solve for y. Since y = x, y = 0 or y = 1, respectively.

So the two points are (0, 0) and (1, 1)

I've shown that on the attached graph.

Answer 2

We can factor this equation like most others:

x - sqrt(x) = 0
sqrt(x)[sqrt(x) - 1] = 0

This means that sqrt(x) = 0, or sqrt(x) - 1 = 0

x = 0 or x = 1.

Since the functions x and sqrt(x) equal each other when x = 0 or x = 1, find the y-value that correspond to these x values.

y = x. If x = 0, y = 0.

Note that sqrt(0) does equal 0.

y = x. If x = 1, y = 1.

Note that sqrt(1) does equal 1.

The points are (0,0) and (1,1)

Answer 3

1) x-x^1/2=0
=> x^1/2(x^1/2-1) =0
=> x^1/2=0
or x^1/2=1


so x=1or 0

2) y=x ..........(1)
y=x^1/2.......(2)
equating, x=x^1/2
solving as 1) we get x=1or 0

hence the reqd point is (1,1), (0, 0)

Answer 4

1)
x - sqrt(x) = 0
x = sqrt(x)
x^2 = x
x = 0
x = 1

y = x
y = sqrt(x)

x = sqrt(x)
x^2 = x
x = 0
x = 1

Intersect when x = 0 and x = 1, therefore at the points (0,0) and (1,1)

Answer 5

1.x^1/2(x^1/2-1)=0
x^1/2=0 or x=0
x^1/2-1=0
x^1/2=1
x=1
x=0 or 1

2.(0,0) is the point of intersection

Answer 6

the number 1 is the only one, maybe zero, too - I'm not sure