baldymcgee6
  • baldymcgee6
Prove that this is true: x*sqrt(x+1) - sqrt(x^2+1)*(x-1) = x^2 - 2x -1
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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baldymcgee6
  • baldymcgee6
\[x*\sqrt(x+1) - \sqrt(x^2+1)*(x-1) = x^2 - 2x -1\]
anonymous
  • anonymous
It isn't.
baldymcgee6
  • baldymcgee6
\[x*\sqrt{x+1} - \sqrt{x^2+1}*(x-1) = x^2 - 2x -1\]

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More answers

baldymcgee6
  • baldymcgee6
that's what i thought too...
anonymous
  • anonymous
if you plug in x = 1 I get sqrt(2) = -2.
baldymcgee6
  • baldymcgee6
k thanks.
calculusfunctions
  • 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.
calculusfunctions
  • 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?
anonymous
  • anonymous
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.
calculusfunctions
  • 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.
baldymcgee6
  • baldymcgee6
@calculusfunctions, no it is not under the root.
calculusfunctions
  • calculusfunctions
Are you sure you copied the question correctly?
calculusfunctions
  • calculusfunctions
Could you please double check because I'd really like to help you if I could.
baldymcgee6
  • baldymcgee6
yep, don't worry about it. It is very possible that they are not equal.
baldymcgee6
  • baldymcgee6
In fact it is so possible that it is true that they are not equal. :)
baldymcgee6
  • baldymcgee6
but thanks for your eagerness to help!
calculusfunctions
  • calculusfunctions
You're right! If LS ≠ RS for some values of x, then the equation is not an identity.
calculusfunctions
  • calculusfunctions
No worries. Welcome!

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