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Find x in tricky equation

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data
    find x in the equation:

    a = x + 1/x


    2. Relevant equations



    3. The attempt at a solution
    I sat down and thought it was easy to do, but was terribly schocked at the fact, that I didn't know how to solve this equation. What is the general approach?
     
  2. jcsd
  3. May 29, 2012 #2

    SammyS

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    Multiplying both sides by x results in a quadratic equation.
     
  4. May 29, 2012 #3

    HallsofIvy

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    If that is 1= x+ (1/x) then multiplying both sides by x gives the quadratic equation [itex]x= x^2+ 1[/itex] which is equivalent to [itex]x^2- x+ 1= 0[/itex]. You will find that it has no real roots.


    If it is, rather, 1= (x+ 1)/x (in which case you should have used parentheses) you can again multiply both sides by x to get x= x+ 1 which is not true for any value of x.
     
    Last edited: May 30, 2012
  5. May 29, 2012 #4

    SammyS

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    If a ≠ 1, then [itex]\displaystyle a=\frac{x+1}{x}[/itex] does have one real root.
     
  6. May 29, 2012 #5
    [Post cleared by myself]
     
    Last edited: May 29, 2012
  7. May 29, 2012 #6
    Ya, I think you are right, I cleared my response.
     
  8. May 30, 2012 #7

    SammyS

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    Please, read the rules for Homework Help this forum. Link

    Your solution is far too complete.
     
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