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Difficult Equation

  1. May 26, 2009 #1
    hey all,

    a friend gave me this equation and required that i solve it:


    I could only solve it graphically and the answer was (x = 4),
    so i wonder if there is an algebraic solution for it ?
  2. jcsd
  3. May 26, 2009 #2


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    I don't think there is any way to solve it algebraically.

    With such equations, it's easy to create them, while terribly annoying to solve without calculators to solve it numerically for you. I think your friend may have caused you a headache for laughs :wink:
    Last edited: May 26, 2009
  4. May 26, 2009 #3
    lol yeah i guess...thanks anyway.
  5. May 26, 2009 #4
    log it, make sqrt(x) the subject, square both sides, and I think that would give you a quadratic which is easy to solve.

    edit: Sorry I just realized that's a dumb idea. Yeah, I don't think there's any way to solve it analytically.
  6. May 26, 2009 #5
    Anyway, not with log and all. Since you have a sum of the two, the log would not apply in that sense.

  7. May 26, 2009 #6
    Calculators use Newton's method to solve equations (including this type of equations of course)
    maybe that's the only analytic way to solve it, but i don't know how to use this method :smile:
  8. May 26, 2009 #7

    matt grime

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    "Algebraically" is a vague term. It is easy to see that if there is a rational answer then it must actually be integral, and in fact x is a square. This leads you to try 1,4 and get the answer (almost) immediately.

    If there isn't such a nice easy to spot idea, then the solution is almost certainly going to be nasty, transcendental and impossible to write down in any nice way, so don't bother to try.
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