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Basic algebra question

  1. Feb 11, 2015 #1
    << Mentor Note -- OP has been advised to type their questions into the forum next time, instead of inserting images >>

    1. The problem statement, all variables and given/known data

    Dear Mentors and PF helpers,

    I have a question from today's lesson.


    2. Relevant equations

    3. The attempt at a solution

    Is 1) and 2) both acceptable? If only of of them is acceptable, is there any reason why?

    Thanks for your time
    Last edited by a moderator: Feb 11, 2015
  2. jcsd
  3. Feb 11, 2015 #2


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    Homework Helper

    Only 2.
    The ## \sqrt{} ## implies that it only returns the positive square root of a number. That is why you will often see ##\pm \sqrt{} ## in formulas.
  4. Feb 11, 2015 #3


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    Science Advisor

    For x any real number, [itex]\sqrt{x^2}= |x|[/itex], NOT [itex]\sqrt{x}= x[/itex]

    That is easily seen by taking x to be any negative number, say x= -2. In that case, [itex]x^2= (-2)^2= 4[/itex] and [itex]\sqrt{x^2}= \sqrt{4}= 2[/itex], NOT -2.
    Last edited by a moderator: Feb 11, 2015
  5. Feb 11, 2015 #4


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    Homework Helper

    However, if you know something about x, like it is positive, then you may use the notation in (1) .
    Also, if you have ##y = x^2##, then ##x = \pm \sqrt{y}##.
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