baldymcgee6 3 years ago Prove that this is true: x*sqrt(x+1) - sqrt(x^2+1)*(x-1) = x^2 - 2x -1

1. baldymcgee6

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

2. Jemurray3

It isn't.

3. baldymcgee6

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

4. baldymcgee6

that's what i thought too...

5. Jemurray3

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

6. baldymcgee6

k thanks.

7. calculusfunctions

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

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

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

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

@calculusfunctions, no it is not under the root.

12. calculusfunctions

Are you sure you copied the question correctly?

13. calculusfunctions

14. baldymcgee6

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

15. baldymcgee6

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

16. baldymcgee6

but thanks for your eagerness to help!

17. calculusfunctions

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

18. calculusfunctions

No worries. Welcome!