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y=4sqwrt(ax+b)³ la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                 3
        _________ 
y = 4*\/ a*x + b
$$y = 4 \left(\sqrt{a x + b}\right)^{3}$$
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Gráfica
Respuesta rápida [src] 
                                                3/4                                                                                               3/4                                               
       /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\       /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\
y1 = 4*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *cos|-----------------------------------------| + 4*I*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *sin|-----------------------------------------|
                                                       \                    2                    /                                                       \                    2                    /
$$y_{1} = 4 i \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)} + 4 \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)}$$ 
y1 = 4*i*((re(b) + re(a*x))^2 + (im(b) + im(a*x))^2)^(3/4)*sin(3*atan2(im(b) + im(a*x, re(b) + re(a*x))/2) + 4*((re(b) + re(a*x))^2 + (im(b) + im(a*x))^2)^(3/4)*cos(3*atan2(im(b) + im(a*x), re(b) + re(a*x))/2))
Suma y producto de raíces [src] 
suma
                                           3/4                                                                                               3/4                                               
  /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\       /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\
4*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *cos|-----------------------------------------| + 4*I*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *sin|-----------------------------------------|
                                                  \                    2                    /                                                       \                    2                    /
$$4 i \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)} + 4 \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)}$$ 
=
                                           3/4                                                                                               3/4                                               
  /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\       /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\
4*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *cos|-----------------------------------------| + 4*I*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *sin|-----------------------------------------|
                                                  \                    2                    /                                                       \                    2                    /
$$4 i \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)} + 4 \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)}$$ 
producto
                                           3/4                                                                                               3/4                                               
  /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\       /                 2                    2\       /3*atan2(im(b) + im(a*x), re(b) + re(a*x))\
4*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *cos|-----------------------------------------| + 4*I*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *sin|-----------------------------------------|
                                                  \                    2                    /                                                       \                    2                    /
$$4 i \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)} + 4 \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2} \right)}$$ 
=
                                                3*I*atan2(im(b) + im(a*x), re(b) + re(a*x))
                                           3/4  -------------------------------------------
  /                 2                    2\                          2                     
4*\(im(b) + im(a*x))  + (re(b) + re(a*x)) /   *e
$$4 \left(\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)}\right)^{2}\right)^{\frac{3}{4}} e^{\frac{3 i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a x\right)},\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(a x\right)} \right)}}{2}}$$ 
4*((im(b) + im(a*x))^2 + (re(b) + re(a*x))^2)^(3/4)*exp(3*i*atan2(im(b) + im(a*x), re(b) + re(a*x))/2)
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