
e^x1/x^2 = 0
hi, i have to solve this equation:
$\displaystyle e^x\frac{1}{x^2}=0$
it put it in wolframalpha and it says that the solution is $\displaystyle 2W(\frac{1}{2})$, where W is the Lambert Wfunction, but i dont know how it find this. Can someone help me to show that the solution is really that? thanks

Re: e^x1/x^2 = 0
$\displaystyle e^x\frac{1}{x^2} = 0$
$\displaystyle e^x=\frac{1}{x^2}$
$\displaystyle x=2lnx$
$\displaystyle \frac{x}{2}=lnx$
$\displaystyle e^{x/2}=\pm \frac{1}{x}$
$\displaystyle \frac{x}{2}.e^{\frac{x}{2}}=\pm \frac{1}{2}$
$\displaystyle \frac{x}{2}.e^{\frac{x}{2}}=\pm \frac{1}{2}$
$\displaystyle \frac{x}{2}=W(\pm \frac{1}{2})$
$\displaystyle x=2W(\pm \frac{1}{2})$