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Simple question,Help

  1. Feb 16, 2010 #1
    2 = sqrt(4) = sqrt(-1*-1*4) = sqrt(-1)*sqrt(-1)*sqrt(4) = -1*sqrt(4) = -2 ?????


    Where am I wrong? sqrt(4) = +2 or -2 in the last step? but see sqrt(4)=-1*sqrt(4), still wrong..

    Thanks in advance
     
  2. jcsd
  3. Feb 16, 2010 #2
    Thanks!,how silly am I.....gosh...
     
  4. Feb 16, 2010 #3
    The real problem here lies in the first step, not the last. 2 is a solution to √4, but is not the solution. Your conundrum has simply re-stated that -2 is also a solution to √4. This string of equations does not prove that 2 = -2 (obviously), only that the solution to √4 is non-unique. Good luck!
     
  5. Feb 16, 2010 #4
    Thanks Unit91Actual!
     
  6. Feb 16, 2010 #5
    [itex] x^2 = 4 [/itex] has two solutions, but sqrt(4) means the positive solution of this equations.
    The other one is -sqrt(4).
    2 = sqrt(-1 * -1 * 4) is OK, but the next step is not since sqrt(A*B) = sqrt(A) * sqrt(B) is only valid if A and B are >= 0
     
  7. Feb 16, 2010 #6
    Good point.
     
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