Thread: Square roots subtraction

I have a problem that says
√x+8) - √x-4) = 2

I don't know how to continue with this problem...



Thank you in advance.

Originally Posted by Joaco

I have a problem that says
√x+8) - √x-4) = 2

I don't know how to continue with this problem...
Thank you in advance.

Do you mean

A. or

B. or

C.


If, as I suspect, the correct expression is A then you will need to square both sides



Simplfying:

Square again:

I'll leave you to finish that off


edit: this equation has only one solution and it is in the domain of the original equation so there can be no extraneous solutions

I would have done that slightly differently. From , add to both sides to get . Squaring both sides of that you get . You still have the square root form the "cross term" but since you don't have both square roots on the same side, it's a little simpler. That can be reduced, by canceling the "x" terms on both sides and canceling the "-4" and "4", to which reduces to . Now square both sides again to get x- 4= 4.

Notice that while e^(i*pi)'s equation looks like a quadratic, it is not be cause the [itex]x^2[/itex] terms on each side will cancel.

Originally Posted by HallsofIvy

I would have done that slightly differently. From , add to both sides to get . Squaring both sides of that you get . You still have the square root form the "cross term" but since you don't have both square roots on the same side, it's a little simpler. That can be reduced, by canceling the "x" terms on both sides and canceling the "-4" and "4", to which reduces to . Now square both sides again to get x- 4= 4.

Notice that while e^(i*pi)'s equation looks like a quadratic, it is not be cause the [itex]x^2[/itex] terms on each side will cancel.

That helped me out a lot, I was stuck at the part until I read your post.
Thank you a lot.


Also thank you a lot .