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cbrt(x)y=x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
3 ___      
\/ x *y = x
x3y=x\sqrt[3]{x} y = x
Simplificar
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
x3y=x\sqrt[3]{x} y = x
Коэффициент при y равен
x3\sqrt[3]{x}
entonces son posibles los casos para x :
x<0x < 0
x=0x = 0
Consideremos todos los casos con detalles:
Con
x<0x < 0
la ecuación será
−13y+1=0\sqrt[3]{-1} y + 1 = 0
su solución
Con
x=0x = 0
la ecuación será
0=00 = 0
su solución
cualquiera y
Gráfica
Respuesta rápida [src] 
        _________________                                   _________________                           
     3 /   2        2        /2*atan2(im(x), re(x))\     3 /   2        2        /2*atan2(im(x), re(x))\
y1 = \/  im (x) + re (x) *cos|---------------------| + I*\/  im (x) + re (x) *sin|---------------------|
                             \          3          /                             \          3          /
y1=i(re⁡(x))2+(im⁡(x))23sin⁡(2atan2⁡(im⁡(x),re⁡(x))3)+(re⁡(x))2+(im⁡(x))23cos⁡(2atan2⁡(im⁡(x),re⁡(x))3)y_{1} = i \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} + \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} 
y1 = i*(re(x)^2 + im(x)^2)^(1/3)*sin(2*atan2(im(x, re(x))/3) + (re(x)^2 + im(x)^2)^(1/3)*cos(2*atan2(im(x), re(x))/3))
Suma y producto de raíces [src] 
suma
   _________________                                   _________________                           
3 /   2        2        /2*atan2(im(x), re(x))\     3 /   2        2        /2*atan2(im(x), re(x))\
\/  im (x) + re (x) *cos|---------------------| + I*\/  im (x) + re (x) *sin|---------------------|
                        \          3          /                             \          3          /
i(re⁡(x))2+(im⁡(x))23sin⁡(2atan2⁡(im⁡(x),re⁡(x))3)+(re⁡(x))2+(im⁡(x))23cos⁡(2atan2⁡(im⁡(x),re⁡(x))3)i \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} + \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} 
=
   _________________                                   _________________                           
3 /   2        2        /2*atan2(im(x), re(x))\     3 /   2        2        /2*atan2(im(x), re(x))\
\/  im (x) + re (x) *cos|---------------------| + I*\/  im (x) + re (x) *sin|---------------------|
                        \          3          /                             \          3          /
i(re⁡(x))2+(im⁡(x))23sin⁡(2atan2⁡(im⁡(x),re⁡(x))3)+(re⁡(x))2+(im⁡(x))23cos⁡(2atan2⁡(im⁡(x),re⁡(x))3)i \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} + \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} 
producto
   _________________                                   _________________                           
3 /   2        2        /2*atan2(im(x), re(x))\     3 /   2        2        /2*atan2(im(x), re(x))\
\/  im (x) + re (x) *cos|---------------------| + I*\/  im (x) + re (x) *sin|---------------------|
                        \          3          /                             \          3          /
i(re⁡(x))2+(im⁡(x))23sin⁡(2atan2⁡(im⁡(x),re⁡(x))3)+(re⁡(x))2+(im⁡(x))23cos⁡(2atan2⁡(im⁡(x),re⁡(x))3)i \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} + \sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{2 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3} \right)} 
=
                      2*I*atan2(im(x), re(x))
   _________________  -----------------------
3 /   2        2                 3           
\/  im (x) + re (x) *e
(re⁡(x))2+(im⁡(x))23e2iatan2⁡(im⁡(x),re⁡(x))3\sqrt[3]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} e^{\frac{2 i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{3}} 
(im(x)^2 + re(x)^2)^(1/3)*exp(2*i*atan2(im(x), re(x))/3)
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