Question

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

Answer 1

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

Answer 2

It isn't.

Answer 3

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

Answer 4

that's what i thought too...

Answer 5

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

Answer 6

k thanks.

Answer 7

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.

Answer 8

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?

Answer 9

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.

Answer 10

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

Answer 11

@calculusfunctions, no it is not under the root.

Answer 12

Are you sure you copied the question correctly?

Answer 13

Could you please double check because I'd really like to help you if I could.

Answer 14

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

Answer 15

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

Answer 16

but thanks for your eagerness to help!

Answer 17

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

Answer 18

No worries. Welcome!