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x^3+y^3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 3    3    
x  + y  = 0
x3+y3=0x^{3} + y^{3} = 0
Simplificar
Teorema de Cardano-Vieta
es ecuación cúbica reducida
py2+qy+v+y3=0p y^{2} + q y + v + y^{3} = 0
donde
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=0q = 0
v=dav = \frac{d}{a}
v=x3v = x^{3}
Fórmulas de Cardano-Vieta
y1+y2+y3=−py_{1} + y_{2} + y_{3} = - p
y1y2+y1y3+y2y3=qy_{1} y_{2} + y_{1} y_{3} + y_{2} y_{3} = q
y1y2y3=vy_{1} y_{2} y_{3} = v
y1+y2+y3=0y_{1} + y_{2} + y_{3} = 0
y1y2+y1y3+y2y3=0y_{1} y_{2} + y_{1} y_{3} + y_{2} y_{3} = 0
y1y2y3=x3y_{1} y_{2} y_{3} = x^{3}
Gráfica
Respuesta rápida [src] 
y1 = -re(x) - I*im(x)
y1=−re⁡(x)−iim⁡(x)y_{1} = - \operatorname{re}{\left(x\right)} - i \operatorname{im}{\left(x\right)} 
               /          ___      \     ___      
     re(x)     |im(x)   \/ 3 *re(x)|   \/ 3 *im(x)
y2 = ----- + I*|----- - -----------| + -----------
       2       \  2          2     /        2
y2=i(−3re⁡(x)2+im⁡(x)2)+re⁡(x)2+3im⁡(x)2y_{2} = i \left(- \frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) + \frac{\operatorname{re}{\left(x\right)}}{2} + \frac{\sqrt{3} \operatorname{im}{\left(x\right)}}{2} 
               /          ___      \     ___      
     re(x)     |im(x)   \/ 3 *re(x)|   \/ 3 *im(x)
y3 = ----- + I*|----- + -----------| - -----------
       2       \  2          2     /        2
y3=i(3re⁡(x)2+im⁡(x)2)+re⁡(x)2−3im⁡(x)2y_{3} = i \left(\frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) + \frac{\operatorname{re}{\left(x\right)}}{2} - \frac{\sqrt{3} \operatorname{im}{\left(x\right)}}{2} 
y3 = i*(sqrt(3)*re(x)/2 + im(x)/2) + re(x)/2 - sqrt(3)*im(x)/2
Suma y producto de raíces [src] 
suma
                             /          ___      \     ___                   /          ___      \     ___      
                   re(x)     |im(x)   \/ 3 *re(x)|   \/ 3 *im(x)   re(x)     |im(x)   \/ 3 *re(x)|   \/ 3 *im(x)
-re(x) - I*im(x) + ----- + I*|----- - -----------| + ----------- + ----- + I*|----- + -----------| - -----------
                     2       \  2          2     /        2          2       \  2          2     /        2
((−re⁡(x)−iim⁡(x))+(i(−3re⁡(x)2+im⁡(x)2)+re⁡(x)2+3im⁡(x)2))+(i(3re⁡(x)2+im⁡(x)2)+re⁡(x)2−3im⁡(x)2)\left(\left(- \operatorname{re}{\left(x\right)} - i \operatorname{im}{\left(x\right)}\right) + \left(i \left(- \frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) + \frac{\operatorname{re}{\left(x\right)}}{2} + \frac{\sqrt{3} \operatorname{im}{\left(x\right)}}{2}\right)\right) + \left(i \left(\frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) + \frac{\operatorname{re}{\left(x\right)}}{2} - \frac{\sqrt{3} \operatorname{im}{\left(x\right)}}{2}\right) 
=
  /          ___      \     /          ___      \          
  |im(x)   \/ 3 *re(x)|     |im(x)   \/ 3 *re(x)|          
I*|----- + -----------| + I*|----- - -----------| - I*im(x)
  \  2          2     /     \  2          2     /
i(−3re⁡(x)2+im⁡(x)2)+i(3re⁡(x)2+im⁡(x)2)−iim⁡(x)i \left(- \frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) + i \left(\frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) - i \operatorname{im}{\left(x\right)} 
producto
                   /          /          ___      \     ___      \ /          /          ___      \     ___      \
                   |re(x)     |im(x)   \/ 3 *re(x)|   \/ 3 *im(x)| |re(x)     |im(x)   \/ 3 *re(x)|   \/ 3 *im(x)|
(-re(x) - I*im(x))*|----- + I*|----- - -----------| + -----------|*|----- + I*|----- + -----------| - -----------|
                   \  2       \  2          2     /        2     / \  2       \  2          2     /        2     /
(−re⁡(x)−iim⁡(x))(i(−3re⁡(x)2+im⁡(x)2)+re⁡(x)2+3im⁡(x)2)(i(3re⁡(x)2+im⁡(x)2)+re⁡(x)2−3im⁡(x)2)\left(- \operatorname{re}{\left(x\right)} - i \operatorname{im}{\left(x\right)}\right) \left(i \left(- \frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) + \frac{\operatorname{re}{\left(x\right)}}{2} + \frac{\sqrt{3} \operatorname{im}{\left(x\right)}}{2}\right) \left(i \left(\frac{\sqrt{3} \operatorname{re}{\left(x\right)}}{2} + \frac{\operatorname{im}{\left(x\right)}}{2}\right) + \frac{\operatorname{re}{\left(x\right)}}{2} - \frac{\sqrt{3} \operatorname{im}{\left(x\right)}}{2}\right) 
=
    3          3          2                  2         
- re (x) + I*im (x) + 3*im (x)*re(x) - 3*I*re (x)*im(x)
−(re⁡(x))3−3i(re⁡(x))2im⁡(x)+3re⁡(x)(im⁡(x))2+i(im⁡(x))3- \left(\operatorname{re}{\left(x\right)}\right)^{3} - 3 i \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + 3 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} + i \left(\operatorname{im}{\left(x\right)}\right)^{3} 
-re(x)^3 + i*im(x)^3 + 3*im(x)^2*re(x) - 3*i*re(x)^2*im(x)
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