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Solution to: Sqrt(x) = -1

  1. Nov 20, 2007 #1
    Does the equation Sqrt(x) + 1 = 0 have a solution? I would say that it doesnt. But the equation x^2 + 1 = 0 doesn't have a solution either, unless you define the imaginary unit i as the solution to the equation.

    So why don't one define some unit which is the solution to the equation Sqrt(x) + 1 = 0? Is it simply because it is of no practical use?
     
  2. jcsd
  3. Nov 20, 2007 #2
    [tex]\sqrt{i^{4}}[/tex] +1 = 0
     
  4. Nov 20, 2007 #3

    HallsofIvy

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    Of course, i4= 1!

    Repetit, if you are referring to the square root function as defined for real numbers, then [itex]\sqrt{x}[/itex] is specifically DEFINED as "the positive real number whose square is x". By that definition, it is impossible that [itex]\sqrt{x}= -1[/itex].

    If, however, you are referring to the square root function as defined for complex numbers, where 'multi-valued' functions are allowed, then -1 is one of the two square roots of 1. The only solution to the equation [itex]\sqrt{x}= -1[/itex] is x= 1.
     
  5. Nov 20, 2007 #4
    Hmm, I see, that makes sense. Thanks to both of you!
     
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