Find the Zeros of the Equation

[Lord Dark]

Homework Statement

i have a problem i tried to solved about 3 days and i couldn't ... here it is :

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

Homework Equations

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 ??

 

[HallsofIvy]

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.

 

[Lord Dark]

thanks very much :)