How many possible solutions can there be?

Question

Solve algebraically and check your potential solutions:
√x+2-x=0

x+2 is supposed to be under the square root sign.

Answer 1

What is under the square root sign? just x or x + 2?

I assume you meant (x + 2) was under the square root.

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

To check:
sqrt (x + 2) - x = 0
sqrt (2 + 2) - (2) = 0
sqrt (4) - 2 = 0
2 - 2 = 0
TRUE

sqrt (x + 2) - x = 0
sqrt (-1 + 2) - (-1) = 0
sqrt (1) + 1 = 0
1 + 1 = 0
FALSE

So, there is only one possible solution (x = 2).

Answer 2

Hey there!

Here's the answer.

sqrt(x+2)-x=0 --> Write the problem.
sqrt(x+2)=x --> Add x to both sides of the equation.
x+2=x^2 --> Square both sides of the equation.
0=x^2-x-2 --> Subtract x+2 on both sides of the equation.
x^2-x-2=0 --> Use symmetric property of equality i.e. if a=b, then b=a.
(x-2)(x+1)=0 --> Factor out the above equation.
x-2=0 or x+1=0 --> Use the zero-product property i.e. if pq=0, then p=0 or q=0.
x=2 or x=-1 Solve each equation for x.

Check to see whether there are any extraneous solutions i.e. solutions which do not satisfy the equation.

sqrt(x+2)-x=0 -->
sqrt(2+2)-2=0 -->
sqrt(4)-2=0 -->
2-2=0 -->
0=0, true.

sqrt(x+2)-x=0 -->
sqrt(-1+2)+1=0 -->
sqrt(1)+1=0 -->
1+1=0 -->
2=0, false.

Since -1 does not satisfy the equation and it is known as an extraneous solution, the solution to the equation is 2.

Hope it helps!

Answer 3

1)x>=0
sqrtx= x-2 sp x-2>=0 and x>=2
squaring
x=x^2-4x+4
x^-5x+4=0 x= ((5+-sqrt(25-16))/2 so x= 4 and x= 1(which can´t be)
There is one solution
If you meant
sqrt(x+2)-x= 0 x+2>=0 s0 x>=-2
sqrt(x-2)=x means x>=0

squaring x+2=x^2 x^-x2-2=0
x=((1+-3)/2 x= 2 and x=-1 This last one as <0 is not solutions

Answer 4

√x - x=-2

Answer 5

sqrt x = u

-u^2 + u + 2 = 0

u^2 - u - 2 = 0

(u - 2)(u+1)

u = -1

u = 2

sqrt x = -1

x = 1

sqrt x = 2

x = 4

Answer 6

that is equal to X^2 - x- 2 = 0
that can be simplified as (x+1)(x-2) = 0

from there, x can either equal 2 or -1

test them out you can see that only 2 works