x^2-2ln(x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
-re(W(-1)) -re(W(-1))
----------- -----------
/im(W(-1))\ 2 2 /im(W(-1))\
x1 = cos|---------|*e - I*e *sin|---------|
\ 2 / \ 2 /
$$x_{1} = e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$
x1 = exp(-re(LambertW(-1))/2)*cos(im(LambertW(-1))/2) - i*exp(-re(LambertW(-1))/2)*sin(im(LambertW(-1))/2)
Suma y producto de raíces
[src]
-re(W(-1)) -re(W(-1))
----------- -----------
/im(W(-1))\ 2 2 /im(W(-1))\
cos|---------|*e - I*e *sin|---------|
\ 2 / \ 2 /
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$
-re(W(-1)) -re(W(-1))
----------- -----------
/im(W(-1))\ 2 2 /im(W(-1))\
cos|---------|*e - I*e *sin|---------|
\ 2 / \ 2 /
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$
-re(W(-1)) -re(W(-1))
----------- -----------
/im(W(-1))\ 2 2 /im(W(-1))\
cos|---------|*e - I*e *sin|---------|
\ 2 / \ 2 /
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \cos{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)} - i e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2}} \sin{\left(\frac{\operatorname{im}{\left(W\left(-1\right)\right)}}{2} \right)}$$
re(W(-1)) I*im(W(-1))
- --------- - -----------
2 2
e
$$e^{- \frac{\operatorname{re}{\left(W\left(-1\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(-1\right)\right)}}{2}}$$
exp(-re(LambertW(-1))/2 - i*im(LambertW(-1))/2)
x1 = 0.91996970492198 - 0.726782465920492*i
x2 = 0.91996970492198 + 0.726782465920492*i
x3 = 0.919969704921981 + 0.726782465920494*i
x4 = 0.919969704921981 + 0.726782465920494*i
x5 = 0.919969704921981 + 0.726782465920494*i
x5 = 0.919969704921981 + 0.726782465920494*i