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2x^2-lnx=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   2             
2*x  - log(x) = 0
$$2 x^{2} - \log{\left(x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                -re(W(-4))       -re(W(-4))                
                -----------      -----------               
   /im(W(-4))\       2                2         /im(W(-4))\
cos|---------|*e            - I*e           *sin|---------|
   \    2    /                                  \    2    /
$$\frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}} - \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}}$$ 
=
                -re(W(-4))       -re(W(-4))                
                -----------      -----------               
   /im(W(-4))\       2                2         /im(W(-4))\
cos|---------|*e            - I*e           *sin|---------|
   \    2    /                                  \    2    /
$$\frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}} - \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}}$$ 
producto
                -re(W(-4))       -re(W(-4))                
                -----------      -----------               
   /im(W(-4))\       2                2         /im(W(-4))\
cos|---------|*e            - I*e           *sin|---------|
   \    2    /                                  \    2    /
$$\frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}} - \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}}$$ 
=
   re(W(-4))   I*im(W(-4))
 - --------- - -----------
       2            2     
e
$$e^{- \frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(-4\right)\right)}}{2}}$$ 
exp(-re(LambertW(-4))/2 - i*im(LambertW(-4))/2)
Respuesta rápida [src] 
                     -re(W(-4))       -re(W(-4))                
                     -----------      -----------               
        /im(W(-4))\       2                2         /im(W(-4))\
x1 = cos|---------|*e            - I*e           *sin|---------|
        \    2    /                                  \    2    /
$$x_{1} = \frac{\cos{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}} - \frac{i \sin{\left(\frac{\operatorname{im}{\left(W\left(-4\right)\right)}}{2} \right)}}{e^{\frac{\operatorname{re}{\left(W\left(-4\right)\right)}}{2}}}$$ 
x1 = exp(-re(LambertW(-4))/2)*cos(im(LambertW(-4))/2) - i*exp(-re(LambertW(-4))/2)*sin(im(LambertW(-4))/2)
Respuesta numérica [src] 
x1 = 0.410801796926384 + 0.581774104948117*i
x2 = 0.410801796926384 - 0.581774104948117*i
x2 = 0.410801796926384 - 0.581774104948117*i
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