x^3+y^3=-61 (x*y+9)*(x+y)=11
Решение
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[LaTeX]
3 3 x + y = -61
$$x^{3} + y^{3} = -61$$
(x*y + 9)*(x + y) = 11
$$\left(x + y\right) \left(x y + 9\right) = 11$$
Быстрый ответ
[LaTeX]
$$x_{1} = -5$$
=
$$-5$$
=
$$y_{1} = 4$$
=
$$4$$
=
=
$$-5$$
=
-5
$$y_{1} = 4$$
=
$$4$$
=
4
$$x_{2} = 4$$
=
$$4$$
=
$$y_{2} = -5$$
=
$$-5$$
=
=
$$4$$
=
4
$$y_{2} = -5$$
=
$$-5$$
=
-5
$$x_{3} = \frac{1}{4} - \frac{\sqrt{111} i}{4} - \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} - \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
$$y_{3} = \frac{1}{4} - \frac{\sqrt{111} i}{4} + \sqrt{\frac{27}{14} - \frac{9 i}{28} \sqrt{111}}$$
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} + \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} - \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
-1.45670526828762 - 1.64180888513963*i
$$y_{3} = \frac{1}{4} - \frac{\sqrt{111} i}{4} + \sqrt{\frac{27}{14} - \frac{9 i}{28} \sqrt{111}}$$
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} + \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
1.95670526828762 - 3.62601799128674*i
$$x_{4} = \frac{1}{4} - \frac{\sqrt{111} i}{4} + \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} + \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
$$y_{4} = \frac{1}{4} - \frac{\sqrt{111} i}{4} - \sqrt{\frac{27}{14} - \frac{9 i}{28} \sqrt{111}}$$
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} - \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} + \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
1.95670526828762 - 3.62601799128674*i
$$y_{4} = \frac{1}{4} - \frac{\sqrt{111} i}{4} - \sqrt{\frac{27}{14} - \frac{9 i}{28} \sqrt{111}}$$
=
$$\frac{1}{4} - \frac{\sqrt{111} i}{4} - \frac{3}{14} \sqrt{42 - 7 \sqrt{111} i}$$
=
-1.45670526828762 - 1.64180888513963*i
$$x_{5} = \frac{1}{4} - \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
$$\frac{1}{4} - \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
$$y_{5} = \frac{1}{4} + \sqrt{\frac{27}{14} + \frac{9 i}{28} \sqrt{111}} + \frac{\sqrt{111} i}{4}$$
=
$$\frac{1}{4} + \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
=
$$\frac{1}{4} - \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
-1.45670526828762 + 1.64180888513963*i
$$y_{5} = \frac{1}{4} + \sqrt{\frac{27}{14} + \frac{9 i}{28} \sqrt{111}} + \frac{\sqrt{111} i}{4}$$
=
$$\frac{1}{4} + \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
1.95670526828762 + 3.62601799128674*i
$$x_{6} = \frac{1}{4} + \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
$$\frac{1}{4} + \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
$$y_{6} = \frac{1}{4} - \sqrt{\frac{27}{14} + \frac{9 i}{28} \sqrt{111}} + \frac{\sqrt{111} i}{4}$$
=
$$\frac{1}{4} - \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
=
$$\frac{1}{4} + \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
1.95670526828762 + 3.62601799128674*i
$$y_{6} = \frac{1}{4} - \sqrt{\frac{27}{14} + \frac{9 i}{28} \sqrt{111}} + \frac{\sqrt{111} i}{4}$$
=
$$\frac{1}{4} - \frac{3}{14} \sqrt{42 + 7 \sqrt{111} i} + \frac{\sqrt{111} i}{4}$$
=
-1.45670526828762 + 1.64180888513963*i
Численный ответ
[LaTeX]
x1 = -5.00000000000000 y1 = 4.00000000000000