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sqrtx-4=sqrta la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
  ___         ___
\/ x  - 4 = \/ a
$$\sqrt{x} - 4 = \sqrt{a}$$
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
                                                   2                                                                                                                                                         
/       _________________                         \       _________________                                    _________________ /       _________________                         \                         
|    4 /   2        2        /atan2(im(a), re(a))\|      /   2        2        2/atan2(im(a), re(a))\       4 /   2        2     |    4 /   2        2        /atan2(im(a), re(a))\|    /atan2(im(a), re(a))\
|4 + \/  im (a) + re (a) *cos|-------------------||  - \/  im (a) + re (a) *sin |-------------------| + 2*I*\/  im (a) + re (a) *|4 + \/  im (a) + re (a) *cos|-------------------||*sin|-------------------|
\                            \         2         //                             \         2         /                            \                            \         2         //    \         2         /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$ 
=
                                                   2                                                                                                                                                         
/       _________________                         \       _________________                                    _________________ /       _________________                         \                         
|    4 /   2        2        /atan2(im(a), re(a))\|      /   2        2        2/atan2(im(a), re(a))\       4 /   2        2     |    4 /   2        2        /atan2(im(a), re(a))\|    /atan2(im(a), re(a))\
|4 + \/  im (a) + re (a) *cos|-------------------||  - \/  im (a) + re (a) *sin |-------------------| + 2*I*\/  im (a) + re (a) *|4 + \/  im (a) + re (a) *cos|-------------------||*sin|-------------------|
\                            \         2         //                             \         2         /                            \                            \         2         //    \         2         /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$ 
producto
                                                   2                                                                                                                                                         
/       _________________                         \       _________________                                    _________________ /       _________________                         \                         
|    4 /   2        2        /atan2(im(a), re(a))\|      /   2        2        2/atan2(im(a), re(a))\       4 /   2        2     |    4 /   2        2        /atan2(im(a), re(a))\|    /atan2(im(a), re(a))\
|4 + \/  im (a) + re (a) *cos|-------------------||  - \/  im (a) + re (a) *sin |-------------------| + 2*I*\/  im (a) + re (a) *|4 + \/  im (a) + re (a) *cos|-------------------||*sin|-------------------|
\                            \         2         //                             \         2         /                            \                            \         2         //    \         2         /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$ 
=
                    _________________                                   _________________                                 
                 4 /   2        2        /atan2(im(a), re(a))\       4 /   2        2        /atan2(im(a), re(a))\        
16 + I*im(a) + 8*\/  im (a) + re (a) *cos|-------------------| + 8*I*\/  im (a) + re (a) *sin|-------------------| + re(a)
                                         \         2         /                               \         2         /
$$8 i \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 8 \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} + 16$$ 
16 + i*im(a) + 8*(im(a)^2 + re(a)^2)^(1/4)*cos(atan2(im(a), re(a))/2) + 8*i*(im(a)^2 + re(a)^2)^(1/4)*sin(atan2(im(a), re(a))/2) + re(a)
Respuesta rápida [src] 
                                                        2                                                                                                                                                         
     /       _________________                         \       _________________                                    _________________ /       _________________                         \                         
     |    4 /   2        2        /atan2(im(a), re(a))\|      /   2        2        2/atan2(im(a), re(a))\       4 /   2        2     |    4 /   2        2        /atan2(im(a), re(a))\|    /atan2(im(a), re(a))\
x1 = |4 + \/  im (a) + re (a) *cos|-------------------||  - \/  im (a) + re (a) *sin |-------------------| + 2*I*\/  im (a) + re (a) *|4 + \/  im (a) + re (a) *cos|-------------------||*sin|-------------------|
     \                            \         2         //                             \         2         /                            \                            \         2         //    \         2         /
$$x_{1} = \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$ 
x1 = ((re(a)^2 + im(a)^2)^(1/4)*cos(atan2(im(a, re(a))/2) + 4)^2 + 2*i*((re(a)^2 + im(a)^2)^(1/4)*cos(atan2(im(a), re(a))/2) + 4)*(re(a)^2 + im(a)^2)^(1/4)*sin(atan2(im(a), re(a))/2) - sqrt(re(a)^2 + im(a)^2)*sin(atan2(im(a), re(a))/2)^2)
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