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Prove x^2 = y^2 if x = y or x = -y

  1. Sep 20, 2007 #1

    DavidSnider

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    Gold Member

    I'm trying to Prove x^2 = y^2 if x = y or x = -y and I'm getting stuck.

    Some different things I think are relevant but can't seem to connect together to form a proof. Am I on the right path?

    Squares are non-negative. 0 ≤ a^2

    x^2 - y^2 = 0

    x^2 - y^2 = (x-y)(x+y)
    = (x-y) * x + (x-y) * y : Distributive Law
    = x^2 - xy + xy - y2 : Distributive Law
    = x^2 - y^2 : Additive Inverse
     
  2. jcsd
  3. Sep 20, 2007 #2

    berkeman

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    Staff: Mentor

    Can you use the fact that (-1)^2 = 1 ?
     
  4. Sep 20, 2007 #3

    DavidSnider

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    Ah! Yes I can. Thank you!
    :approve:
     
  5. Sep 20, 2007 #4

    D H

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    Stop here. Don't go any further. What does (x-y)(x+y) = 0 tell you?
     
  6. Sep 20, 2007 #5

    DavidSnider

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    That the difference between x and y multiplied by the sum of x and y is equal to zero

    So.. let's say that (x-y) is M and (X+Y) is N then M * N = 0.

    The only way for this to happen is if one or both of those is equal to 0.
    (x-y) can only be zero if X = Y. X+Y can only be zero if X = -Y.

    Is there a better way I should be expressing that?
     
  7. Sep 20, 2007 #6

    D H

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    You got it.
     
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