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.

Printable View

- Sep 12th 2010, 12:45 PMJoacoSquare 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. - Sep 12th 2010, 12:52 PMe^(i*pi)
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 - Sep 12th 2010, 01:45 PMHallsofIvy
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. - Sep 12th 2010, 02:22 PMJoaco