Help understand radival equations?
When i solve x+6=radical(x+12) on the calculator.. i get -3 which is a solution that works.

Howevet if i square both sides and solve it algebraically. Why do i get a extraneous solution of -8?

Question

Help understand radival equations?
When i solve x+6=radical(x+12) on the calculator.. i get -3 which is a solution that works.

Howevet if i square both sides and solve it algebraically. Why do i get a extraneous solution of -8?

solomonzelman · Answer

you mean,
$\large\color{black}{  x+6=\sqrt{x+12}  }$  ?

solomonzelman · Answer

yes, -3 is the correct solution.

solomonzelman · Answer

but what is your question then?

solomonzelman · Answer

oh, I see, you want to actually work the solutions, right?

anonymous · Answer

Im just wondee why i get anothet solution when i do it algebraically

anonymous · Answer

Cause i get -8 and when i plug it in to the original problem i get 2=-2 which means -8 is not a solution

loser66 · Answer

The right hand side must be $\geq 0$, that is the left hand side must be $\geq 0$ also.
To have it, solve $x+6\geq 0\rightarrow x\geq -6$, That allows you reject x=-8 , since $-8 < -6$

anonymous · Answer

Oh

anonymous · Answer

Wait, but why does squaring it give another solution?

loser66 · Answer

Nope, it gives you 2 solutions which are -3 and -8. You checked and knew -8 is not a solution but you don't know how to get rid of. My logic gives you a key.