x^2+y^2=13 x*y=7
Решение
Быстрый ответ
$$x_{1} = - \frac{1}{7} \left(-13 + \left(- \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)^{2}\right) \left(- \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)$$
=
$$- \frac{\sqrt{7}}{14} \left(13 - 3 \sqrt{3} i\right) e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
$$y_{1} = - \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$- \sqrt{7} e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
=
$$- \frac{\sqrt{7}}{14} \left(13 - 3 \sqrt{3} i\right) e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
-2.59807621135332 + 0.5*i
$$y_{1} = - \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$- \sqrt{7} e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
-2.59807621135332 - 0.5*i
$$x_{2} = - \frac{1}{7} \left(-13 + \left(- \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)^{2}\right) \left(- \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)$$
=
$$- \frac{\sqrt{7}}{14} \left(13 + 3 \sqrt{3} i\right) e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
$$y_{2} = - \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$- \sqrt{7} e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
=
$$- \frac{\sqrt{7}}{14} \left(13 + 3 \sqrt{3} i\right) e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
-2.59807621135332 - 0.5*i
$$y_{2} = - \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$- \sqrt{7} e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
-2.59807621135332 + 0.5*i
$$x_{3} = - \frac{1}{7} \left(-13 + \left(\sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)^{2}\right) \left(\sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)$$
=
$$\frac{\sqrt{7}}{14} \left(13 + 3 \sqrt{3} i\right) e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
$$y_{3} = \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$\sqrt{7} e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
=
$$\frac{\sqrt{7}}{14} \left(13 + 3 \sqrt{3} i\right) e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
2.59807621135332 + 0.5*i
$$y_{3} = \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} - \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$\sqrt{7} e^{- \frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
2.59807621135332 - 0.5*i
$$x_{4} = - \frac{1}{7} \left(-13 + \left(\sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)^{2}\right) \left(\sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}\right)$$
=
$$\frac{\sqrt{7}}{14} \left(13 - 3 \sqrt{3} i\right) e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
$$y_{4} = \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$\sqrt{7} e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
=
$$\frac{\sqrt{7}}{14} \left(13 - 3 \sqrt{3} i\right) e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
2.59807621135332 - 0.5*i
$$y_{4} = \sqrt{7} \cos{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )} + \sqrt{7} i \sin{\left (\frac{1}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )} \right )}$$
=
$$\sqrt{7} e^{\frac{i}{2} \operatorname{atan}{\left (\frac{3 \sqrt{3}}{13} \right )}}$$
=
2.59807621135332 + 0.5*i