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Elementary Equation solving mind-block

  1. Jun 19, 2007 #1
    Hi I have some problems with really basic equations (really elementary)

    Let's say in order to solve an equation [TEX]f(x)=0[/TEX], we multiply the equation by [TEX]x[/TEX]. Therefore we conclude that x can never be =0. But what if at the end step we conclude that [TEX]x=0[/TEX] (maybe along with other solutions)? Do we reject the answer and accept the others? Or is our method of solving the equation incorrect?

    I do know that it is quite impossible for you to arrive at [TEX]x=0[/TEX] after you multiply [TEX]x[/TEX] throughout in order to solve the equation, as that would mean you had introduced an unnecessary common multiple into the equation..
  2. jcsd
  3. Jun 19, 2007 #2


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    Why would we conclude that?

    I'm not at all clear what you are saying here. Certainly if you just take an arbitrary equation, say x2= 0, and multiply both sides by x, you can arrive at x= 0: x3= 0 so x= 0. You may be thinking of an equation in which you have good reason to multiply by x- say something like (x-1)/x= 0. In that case, even before you multiply by x, you know that x= 0 cannot be a solution.
    It is well known that if you multiply both sides of an equation by any function of x, you may introduce "extraneous" roots: numbers that satisfy the new equation but not the original. The only way to be sure is to check the numbers in the original equation.
  4. Jul 8, 2007 #3
    Alright thanks. Sorry for not visiting this thread after so long.
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