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B Square root inquiry

  1. Sep 6, 2016 #1
    Let's say there's an equation

    0 = √x - √x

    I intend to make x the subject of the equation; however because it is a square root, there are numerous solutions; however can I just assume that

    0= √x - -√x= 2√x

    Can I now just rearrange this equation to make x the subject? In other words is the equation above equivalent to the equation below?

    0= -√x -√x = -2√x

    Would the same be true if there were roots in a quadratic equation?
  2. jcsd
  3. Sep 6, 2016 #2


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    Staff: Mentor

    Do you really expect that a-a=2a in general? Here a=sqrt(x).

    What do you know about the solutions to the equation 0=a-a?
  4. Sep 6, 2016 #3
    If something equals 0, you can flip the sign any way you want.
    If x = 0, then -x = 0 as well
  5. Sep 6, 2016 #4
    I think that as this applies to any number; the solutions is any number and therefore the equation is undefined.
  6. Sep 6, 2016 #5


    Staff: Mentor

    Do you realize that the right side is equal to zero for any nonnegative real number x?
    Not sure what you mean by this. The symbol ##\sqrt{x}## has one value, assuming that ##x \ge 0##.
    This is different from the equation you have at the top of your post.
    The first equation you show is √x - √x = 0. The equation just above, when simplified is √x + √x = 0. These two equations are not equivalent.
    I don't understand what you're asking here.
  7. Sep 6, 2016 #6
    I apologise for I am unable to express what I mean; this thread serves no purpose
  8. Sep 6, 2016 #7


    Staff: Mentor

    Thread closed.
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