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Why does a = -a?

  1. Oct 16, 2014 #1
    I've been messing around with numbers (as you do) and I'm wondering why this occurs..
    lets let a = b-c.
    √a
    = √(b-c)
    =√(-(c-b))
    =i√(c-b)
    =i√(-(b-c))
    =i2√(b-c)
    =-√(b-c)
    =-√a
    For example if you let a = 1, b = 2, and c = 1.
     
  2. jcsd
  3. Oct 16, 2014 #2

    Mark44

    Staff: Mentor

    The step above is where the problem is. You're using the property that ##\sqrt{ab} = \sqrt{a}\sqrt{b}##
    There are restrictions on this and some of the other square root properties - both a and b have to be nonnegative.
     
    Last edited: Oct 16, 2014
  4. Oct 16, 2014 #3
    That makes sense. Thanks.
     
  5. Oct 18, 2014 #4

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    [itex]\sqrt[2]{-1} = \pm i. [/itex] The choice of the '+' or '-' depends on the situation. So your result is '[itex] a = \pm a [/itex]' where you must decide which sign is correct.
     
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