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Find the mistake 1=-1 ?

  1. Jun 14, 2010 #1
    Somebody find the mistake here:

    [tex]
    1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{(-1)^2}=-1 \Rightarrow 1=-1
    [/tex]​
     
  2. jcsd
  3. Jun 14, 2010 #2

    Borek

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    Staff: Mentor

    Square root of 1 is not 1, it is either 1 or -1.
     
  4. Jun 14, 2010 #3

    DaveC426913

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    Gold Member

    Since when is the (square root of -1)-squared equal to -1?

    -1 squared is 1.
    The root of 1 is 1, not -1.
     
  5. Jun 14, 2010 #4
    yes it's -1 because (-1)^2=1 from the definition ;)
     
  6. Jun 14, 2010 #5

    DaveC426913

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    So do you or do you not see the flaw?
     
  7. Jun 14, 2010 #6
    The error is here
    [tex]
    \sqrt{(-1)^2} \neq -1
    [/tex]

    [tex]\sqrt{(-1)^2} = |-1|=1[/tex]
     
  8. Jun 14, 2010 #7
    Well-done Njama, your answer is the correct one.
     
  9. Jun 14, 2010 #8

    DaveC426913

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    Which is precisely what I said in post 3.
     
  10. Jun 14, 2010 #9

    HallsofIvy

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    Not true.
    Not true.
    True! [tex]\sqrt{x}[/itex], as a real valued function, must have only one value for each x and it is defined as "the positive number y such that [itex]y^2= x[/itex]"
    Then why did you deny it in your post quoted above?
     
  11. Jun 14, 2010 #10

    Redbelly98

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    Is it just me, or is this the 3rd time in the last month somebody has posted the very same 1=-1 argument?
     
  12. Jun 14, 2010 #11

    DaveC426913

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    Gold Member

    Well, it really belongs in the Riddles section.
     
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