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sqrt(x-2)+sqrt(y-2)=2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
  _______     _______    
\/ x - 2  + \/ y - 2  = 2
x−2+y−2=2\sqrt{x - 2} + \sqrt{y - 2} = 2
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Gráfica
Suma y producto de raíces [src] 
suma
                                                                    2                                                                                                                                                                                              
    /        ________________________                              \       ________________________                                         ________________________ /        ________________________                              \                              
    |     4 /             2     2        /atan2(im(y), -2 + re(y))\|      /             2     2        2/atan2(im(y), -2 + re(y))\       4 /             2     2     |     4 /             2     2        /atan2(im(y), -2 + re(y))\|    /atan2(im(y), -2 + re(y))\
2 + |-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||  - \/  (-2 + re(y))  + im (y) *sin |------------------------| + 2*I*\/  (-2 + re(y))  + im (y) *|-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||*sin|------------------------|
    \                                    \           2            //                                    \           2            /                                   \                                    \           2            //    \           2            /
((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)2+2i((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)(re⁡(y)−2)2+(im⁡(y))24sin⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−(re⁡(y)−2)2+(im⁡(y))2sin⁡2(atan2⁡(im⁡(y),re⁡(y)−2)2)+2\left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2 
=
                                                                    2                                                                                                                                                                                              
    /        ________________________                              \       ________________________                                         ________________________ /        ________________________                              \                              
    |     4 /             2     2        /atan2(im(y), -2 + re(y))\|      /             2     2        2/atan2(im(y), -2 + re(y))\       4 /             2     2     |     4 /             2     2        /atan2(im(y), -2 + re(y))\|    /atan2(im(y), -2 + re(y))\
2 + |-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||  - \/  (-2 + re(y))  + im (y) *sin |------------------------| + 2*I*\/  (-2 + re(y))  + im (y) *|-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||*sin|------------------------|
    \                                    \           2            //                                    \           2            /                                   \                                    \           2            //    \           2            /
((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)2+2i((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)(re⁡(y)−2)2+(im⁡(y))24sin⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−(re⁡(y)−2)2+(im⁡(y))2sin⁡2(atan2⁡(im⁡(y),re⁡(y)−2)2)+2\left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2 
producto
                                                                    2                                                                                                                                                                                              
    /        ________________________                              \       ________________________                                         ________________________ /        ________________________                              \                              
    |     4 /             2     2        /atan2(im(y), -2 + re(y))\|      /             2     2        2/atan2(im(y), -2 + re(y))\       4 /             2     2     |     4 /             2     2        /atan2(im(y), -2 + re(y))\|    /atan2(im(y), -2 + re(y))\
2 + |-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||  - \/  (-2 + re(y))  + im (y) *sin |------------------------| + 2*I*\/  (-2 + re(y))  + im (y) *|-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||*sin|------------------------|
    \                                    \           2            //                                    \           2            /                                   \                                    \           2            //    \           2            /
((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)2+2i((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)(re⁡(y)−2)2+(im⁡(y))24sin⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−(re⁡(y)−2)2+(im⁡(y))2sin⁡2(atan2⁡(im⁡(y),re⁡(y)−2)2)+2\left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2 
=
                         _______________________________                                                                           _______________________________                                                                             
                        /       2        2                      _______________________________                                   /       2        2                              _______________________________                              
    re(y)             \/  4 + im (y) + re (y) - 4*re(y)      4 /       2        2                  /atan2(im(y), -2 + re(y))\   \/  4 + im (y) + re (y) - 4*re(y) *re(y)       4 /       2        2                  /atan2(im(y), -2 + re(y))\
5 + ----- + I*im(y) - ---------------------------------- - 4*\/  4 + im (y) + re (y) - 4*re(y) *cos|------------------------| + ---------------------------------------- - 4*I*\/  4 + im (y) + re (y) - 4*re(y) *sin|------------------------|
      2                     ________________________                                               \           2            /             ________________________                                                   \           2            /
                           /             2     2                                                                                         /             2     2                                                                                 
                         \/  (-2 + re(y))  + im (y)                                                                                  2*\/  (-2 + re(y))  + im (y)
−4i(re⁡(y))2−4re⁡(y)+(im⁡(y))2+44sin⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−4(re⁡(y))2−4re⁡(y)+(im⁡(y))2+44cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)+re⁡(y)2+iim⁡(y)+5+(re⁡(y))2−4re⁡(y)+(im⁡(y))2+4re⁡(y)2(re⁡(y)−2)2+(im⁡(y))2−(re⁡(y))2−4re⁡(y)+(im⁡(y))2+4(re⁡(y)−2)2+(im⁡(y))2- 4 i \sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 4 \sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + \frac{\operatorname{re}{\left(y\right)}}{2} + i \operatorname{im}{\left(y\right)} + 5 + \frac{\sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4} \operatorname{re}{\left(y\right)}}{2 \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} - \frac{\sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4}}{\sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} 
5 + re(y)/2 + i*im(y) - sqrt(4 + im(y)^2 + re(y)^2 - 4*re(y))/sqrt((-2 + re(y))^2 + im(y)^2) - 4*(4 + im(y)^2 + re(y)^2 - 4*re(y))^(1/4)*cos(atan2(im(y), -2 + re(y))/2) + sqrt(4 + im(y)^2 + re(y)^2 - 4*re(y))*re(y)/(2*sqrt((-2 + re(y))^2 + im(y)^2)) - 4*i*(4 + im(y)^2 + re(y)^2 - 4*re(y))^(1/4)*sin(atan2(im(y), -2 + re(y))/2)
Respuesta rápida [src] 
                                                                         2                                                                                                                                                                                              
         /        ________________________                              \       ________________________                                         ________________________ /        ________________________                              \                              
         |     4 /             2     2        /atan2(im(y), -2 + re(y))\|      /             2     2        2/atan2(im(y), -2 + re(y))\       4 /             2     2     |     4 /             2     2        /atan2(im(y), -2 + re(y))\|    /atan2(im(y), -2 + re(y))\
x1 = 2 + |-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||  - \/  (-2 + re(y))  + im (y) *sin |------------------------| + 2*I*\/  (-2 + re(y))  + im (y) *|-2 + \/  (-2 + re(y))  + im (y) *cos|------------------------||*sin|------------------------|
         \                                    \           2            //                                    \           2            /                                   \                                    \           2            //    \           2            /
x1=((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)2+2i((re⁡(y)−2)2+(im⁡(y))24cos⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−2)(re⁡(y)−2)2+(im⁡(y))24sin⁡(atan2⁡(im⁡(y),re⁡(y)−2)2)−(re⁡(y)−2)2+(im⁡(y))2sin⁡2(atan2⁡(im⁡(y),re⁡(y)−2)2)+2x_{1} = \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} - 2 \right)}}{2} \right)} + 2 
x1 = (((re(y) - 2)^2 + im(y)^2)^(1/4)*cos(atan2(im(y, re(y) - 2)/2) - 2)^2 + 2*i*(((re(y) - 2)^2 + im(y)^2)^(1/4)*cos(atan2(im(y), re(y) - 2)/2) - 2)*((re(y) - 2)^2 + im(y)^2)^(1/4)*sin(atan2(im(y), re(y) - 2)/2) - sqrt((re(y) - 2)^2 + im(y)^2)*sin(atan2(im(y), re(y) - 2)/2)^2 + 2)
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