Question

√(x+4)-√(x+1)=1

Answer 1

trying to solve for x?

Answer 2

the answer is supposed to be x=0 but I don't know why

Answer 3

Move one radical to the other side of the equation and then square each side. Remember that the right side will be a binomial so you will need to FOIL it. You will get a radical in the product so you will need to isolate it and solve it the same way by squaring each side.

Answer 4

so when you move the radical over, your new equation is:
√(x+4)=1+√(x+1)

Answer 5

Yup. Now square each side. FOIL the right side.

Answer 6

the left side just "pops" out as x+4?

Answer 7

yes. lovely isn't it?

Answer 8

yes, I'm making it overly complicated.

Answer 9

you'll get this and then combine like terms and isolate the radical again.
\[x+4=x+1+2\sqrt{(x+1)} + 1\]

Answer 10

I'm afraid you lost me again.

Answer 11

This is what you get when you square both sides.

Answer 12

but then if you tried to get stuff over on the left, your x disappears...

Answer 13

It's OK because you still have one under the radical. Did you get \[2=2\sqrt{(x+1)}\]

Answer 14

yes, then do you get 4=4(x+1)?

Answer 15

I would've divided both sides by 2 first, but you'll still get x=0 in the end.

Answer 16

alright, let me try it that way then...I did not get to 0....

Answer 17

YES!! Got it! Thank you so much for the step by step!!

Answer 18

After dividing both sides by 2, you'll get \[1=\sqrt{(x+1)}\]

Answer 19

YAY! Good luck!

Answer 20

Lifesaver!