SOLUTION: Solve algebraically? Solve algebraically and check your potential solutions: squareroot(x+2) -x=0 I know that the answers are x=2, x=How do I know for sure they are correct aft

Question 122042: Solve algebraically?
Solve algebraically and check your potential solutions:
squareroot(x+2) -x=0
I know that the answers are x=2, x=How do I know for sure they are correct after checking them. X=2 works out but x=-1 is funny. Thanks

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I presume you solved this in the following fashion:

Square both sides:

or

The reason that doesn't check () is that you introduced an extraneous root when you squared both sides of the equation in the process of solving it. is the only element of the solution set of the original equation.

The following is a trivial example of what happens when you square both sides of an equation:

Let

Square both sides:

or

is fine, but , by substitution in the original equation, leads us to the absurdity that . Therefore is an extraneous root introduced in the process of squaring both sides of the equation and it must be excluded from the solution set.
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