Дано

$$x^{3} – 12 x = 5$$
Ответ

/ / _____ / / / _____ / / _____ / / _____
| |/ 231 || | | |/ 231 || | |/ 231 ||| | |/ 231 ||
|atan|——-|| | |atan|——-|| |atan|——-||| |atan|——-||
| 5 /| / 1 | | 5 /| / 1 ___ | 5 /|| ___ | 5 /|
x1 = – cos|————-| + 4*re|————————————| + I*|- sin|————-| + 4*im|————————————| – / 3 *cos|————-|| + / 3 *sin|————-|
3 / | _______________| | 3 / | _______________| 3 /| 3 /
|/ ___ / _____ | | |/ ___ / _____ | |
|| 1 I*/ 3 | / 5 I*/ 231 | | || 1 I*/ 3 | / 5 I*/ 231 | |
||- – – ——-|*3 / – + ——— | | ||- – – ——-|*3 / – + ——— | |
2 2 / / 2 2 / 2 2 / / 2 2 / /

$$x_{1} = – cos{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )} + 4 Re{left(frac{1}{left(- frac{1}{2} – frac{sqrt{3} i}{2}right) sqrt[3]{frac{5}{2} + frac{sqrt{231} i}{2}}}right)} + sqrt{3} sin{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )} + i left(- sqrt{3} cos{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )} – sin{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )} + 4 Im{left(frac{1}{left(- frac{1}{2} – frac{sqrt{3} i}{2}right) sqrt[3]{frac{5}{2} + frac{sqrt{231} i}{2}}}right)}right)$$

/ / _____ / / / _____ / / _____ / / _____
| |/ 231 || | | |/ 231 || | |/ 231 ||| | |/ 231 ||
|atan|——-|| | |atan|——-|| |atan|——-||| |atan|——-||
| 5 /| / 1 | | 5 /| / 1 ___ | 5 /|| ___ | 5 /|
x2 = – cos|————-| + 4*re|————————————| + I*|- sin|————-| + 4*im|————————————| + / 3 *cos|————-|| – / 3 *sin|————-|
3 / | _______________| | 3 / | _______________| 3 /| 3 /
|/ ___ / _____ | | |/ ___ / _____ | |
|| 1 I*/ 3 | / 5 I*/ 231 | | || 1 I*/ 3 | / 5 I*/ 231 | |
||- – + ——-|*3 / – + ——— | | ||- – + ——-|*3 / – + ——— | |
2 2 / / 2 2 / 2 2 / / 2 2 / /

$$x_{2} = 4 Re{left(frac{1}{left(- frac{1}{2} + frac{sqrt{3} i}{2}right) sqrt[3]{frac{5}{2} + frac{sqrt{231} i}{2}}}right)} – cos{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )} – sqrt{3} sin{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )} + i left(4 Im{left(frac{1}{left(- frac{1}{2} + frac{sqrt{3} i}{2}right) sqrt[3]{frac{5}{2} + frac{sqrt{231} i}{2}}}right)} – sin{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )} + sqrt{3} cos{left (frac{1}{3} {atan}{left (frac{sqrt{231}}{5} right )} right )}right)$$

_______________
/ _____
/ 5 I*/ 231 4
x3 = 3 / – + ——— + ——————–
/ 2 2 _______________
/ _____
/ 5 I*/ 231
3 / – + ———
/ 2 2

$$x_{3} = frac{4}{sqrt[3]{frac{5}{2} + frac{sqrt{231} i}{2}}} + sqrt[3]{frac{5}{2} + frac{sqrt{231} i}{2}}$$
Читайте также  x/5+7=16
Численный ответ

x1 = -3.23319369349000

x2 = -0.422972692468000

x3 = 3.65616638596000

   
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glugovsky
Основные виды работ: рефераты, доклады, решение задач, эссэ, курсовые, дипломные. Знание языков: русский, украинский, английский.