## baldymcgee6 Group Title Prove that this is true: x*sqrt(x+1) - sqrt(x^2+1)*(x-1) = x^2 - 2x -1 one year ago one year ago

1. baldymcgee6 Group Title

$x*\sqrt(x+1) - \sqrt(x^2+1)*(x-1) = x^2 - 2x -1$

2. Jemurray3 Group Title

It isn't.

3. baldymcgee6 Group Title

$x*\sqrt{x+1} - \sqrt{x^2+1}*(x-1) = x^2 - 2x -1$

4. baldymcgee6 Group Title

that's what i thought too...

5. Jemurray3 Group Title

if you plug in x = 1 I get sqrt(2) = -2.

6. baldymcgee6 Group Title

k thanks.

7. calculusfunctions Group Title

By proving that L.S. = R.S. we're proving that it is an identity. Which implies that the equation is valid for all x except x > -1. Therefore Jemurray is correct.

8. calculusfunctions Group Title

Let me ask you though. Do you mean for the (x − 1) to be inside the square root in the second term of the left side of the equation?

9. Jemurray3 Group Title

Even if he did, it doesn't matter. The fact that the first term on the left is only valid on a restricted domain and the others aren't is enough to show that it can't be an equality.

10. calculusfunctions Group Title

I know that but I'm grasping for straws trying to understand what he's talking about or even if asked the question correctly.

11. baldymcgee6 Group Title

@calculusfunctions, no it is not under the root.

12. calculusfunctions Group Title

Are you sure you copied the question correctly?

13. calculusfunctions Group Title

14. baldymcgee6 Group Title

yep, don't worry about it. It is very possible that they are not equal.

15. baldymcgee6 Group Title

In fact it is so possible that it is true that they are not equal. :)

16. baldymcgee6 Group Title

but thanks for your eagerness to help!

17. calculusfunctions Group Title

You're right! If LS ≠ RS for some values of x, then the equation is not an identity.

18. calculusfunctions Group Title

No worries. Welcome!