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Find the Zeros of the Equation

  1. Apr 11, 2009 #1
    1. The problem statement, all variables and given/known data
    i have a problem i tried to solved about 3 days and i couldn't ... here it is :

    (exp(x)/x^3)=2x+1

    2. Relevant equations



    3. The attempt at a solution
    ((e^x)/(x^3))=2x+1 > e^x=2x^4+x^3 >> (x=ln(2x^4+x^3) or 2x^4+x^3-e^x=0) ,, is it possible to get the zeros from the 2 solutions without graphing ??
     
  2. jcsd
  3. Apr 11, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    There is not going to be any "algebraic" method of solving that. You might be able to put it in terms of the Lambert W function but that's probably not what you want. Generally speaking, equations that involve the unknown variable both inside and outside a transcendental function require either "special functions", such as the Lambert W, or numerical solutions, such as graphing.
     
  4. Apr 11, 2009 #3
    thanks very much :)
     
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