Дано
$$x^{4} – y^{4} – 65 = 0$$
Ответ
$$x_{1} = sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} sin{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )} – i sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} cos{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )}$$
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/ 2 2 / / 3 3 4 4 2 2 / 2 2 / / 3 3 4 4 2 2
8 / / 3 3 / 4 4 2 2 |atan2 – 4*im (y)*re(y) + 4*re (y)*im(y), 65 + im (y) + re (y) – 6*im (y)*re (y)/| 8 / / 3 3 / 4 4 2 2 |atan2 – 4*im (y)*re(y) + 4*re (y)*im(y), 65 + im (y) + re (y) – 6*im (y)*re (y)/|
x2 = – / – 4*im (y)*re(y) + 4*re (y)*im(y)/ + 65 + im (y) + re (y) – 6*im (y)*re (y)/ *sin|——————————————————————————–| + I*/ – 4*im (y)*re(y) + 4*re (y)*im(y)/ + 65 + im (y) + re (y) – 6*im (y)*re (y)/ *cos|——————————————————————————–|
4 / 4 /
$$x_{2} = – sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} sin{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )} + i sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} cos{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )}$$
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/ 2 2 / / 3 3 4 4 2 2 / 2 2 / / 3 3 4 4 2 2
8 / / 3 3 / 4 4 2 2 |atan2 – 4*im (y)*re(y) + 4*re (y)*im(y), 65 + im (y) + re (y) – 6*im (y)*re (y)/| 8 / / 3 3 / 4 4 2 2 |atan2 – 4*im (y)*re(y) + 4*re (y)*im(y), 65 + im (y) + re (y) – 6*im (y)*re (y)/|
x3 = – / – 4*im (y)*re(y) + 4*re (y)*im(y)/ + 65 + im (y) + re (y) – 6*im (y)*re (y)/ *cos|——————————————————————————–| – I*/ – 4*im (y)*re(y) + 4*re (y)*im(y)/ + 65 + im (y) + re (y) – 6*im (y)*re (y)/ *sin|——————————————————————————–|
4 / 4 /
$$x_{3} = – i sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} sin{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )} – sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} cos{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )}$$
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/ 2 2 / / 3 3 4 4 2 2 / 2 2 / / 3 3 4 4 2 2
8 / / 3 3 / 4 4 2 2 |atan2 – 4*im (y)*re(y) + 4*re (y)*im(y), 65 + im (y) + re (y) – 6*im (y)*re (y)/| 8 / / 3 3 / 4 4 2 2 |atan2 – 4*im (y)*re(y) + 4*re (y)*im(y), 65 + im (y) + re (y) – 6*im (y)*re (y)/|
x4 = / – 4*im (y)*re(y) + 4*re (y)*im(y)/ + 65 + im (y) + re (y) – 6*im (y)*re (y)/ *cos|——————————————————————————–| + I*/ – 4*im (y)*re(y) + 4*re (y)*im(y)/ + 65 + im (y) + re (y) – 6*im (y)*re (y)/ *sin|——————————————————————————–|
4 / 4 /
$$x_{4} = i sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} sin{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )} + sqrt[8]{left(4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3}right)^{2} + left(left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65right)^{2}} cos{left (frac{1}{4} {atan_{2}}{left (4 left(Re{y}right)^{3} Im{y} – 4 Re{y} left(Im{y}right)^{3},left(Re{y}right)^{4} – 6 left(Re{y}right)^{2} left(Im{y}right)^{2} + left(Im{y}right)^{4} + 65 right )} right )}$$
