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Expresiones idénticas
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- 1.377 multiplicar por x al cubo más 13.299 multiplicar por x al cuadrado menos 33.385 multiplicar por x menos 193.69 es igual a 0
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- 1.377*x3+13.299*x2-33.385*x-193.69=0
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- 1.377*x^3+13.299*x^2-33.385*x-193.69=O
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Expresiones semejantes
- 1.377*x^3-13.299*x^2-33.385*x-193.69=0
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- 1.377*x^3+13.299*x^2+33.385*x-193.69=0
1.377*x^3+13.299*x^2-33.385*x-193.69=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 1377*x 13299*x 6677*x 19369 ------- + -------- - ------ - ----- = 0 1000 1000 200 100
$$\left(- \frac{6677 x}{200} + \left(\frac{1377 x^{3}}{1000} + \frac{13299 x^{2}}{1000}\right)\right) - \frac{19369}{100} = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- \frac{6677 x}{200} + \left(\frac{1377 x^{3}}{1000} + \frac{13299 x^{2}}{1000}\right)\right) - \frac{19369}{100} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{4433 x^{2}}{459} - \frac{33385 x}{1377} - \frac{193690}{1377} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{4433}{459}$$
$$q = \frac{c}{a}$$
$$q = - \frac{33385}{1377}$$
$$v = \frac{d}{a}$$
$$v = - \frac{193690}{1377}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{4433}{459}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{33385}{1377}$$
$$x_{1} x_{2} x_{3} = - \frac{193690}{1377}$$
$$\left(- \frac{6677 x}{200} + \left(\frac{1377 x^{3}}{1000} + \frac{13299 x^{2}}{1000}\right)\right) - \frac{19369}{100} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{4433 x^{2}}{459} - \frac{33385 x}{1377} - \frac{193690}{1377} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{4433}{459}$$
$$q = \frac{c}{a}$$
$$q = - \frac{33385}{1377}$$
$$v = \frac{d}{a}$$
$$v = - \frac{193690}{1377}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{4433}{459}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{33385}{1377}$$
$$x_{1} x_{2} x_{3} = - \frac{193690}{1377}$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
34975204*re|-------------------------------------------------------------| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| / / ____________________\\ / / ____________________\\
| ________________________________________| | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||
|/ ___\ / ____________________ | | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| |atan|--------------------------|| |atan|--------------------------||
|| 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | _________ | \ 10758961249 /| __________ | \ 10758961249 /|| __________ | \ 10758961249 /| _________ | \ 10758961249 /|
||- - - -------|*3 / ----------- + ------------------------ | | ||- - - -------|*3 / ----------- + ------------------------ | \/ 8743801 *sin|--------------------------------| \/ 26231403 *cos|--------------------------------|| \/ 26231403 *sin|--------------------------------| \/ 8743801 *cos|--------------------------------|
4433 \\ 2 2 / \/ 193405158 421362 / | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = - ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| - -------------------------------------------------- + -------------------------------------------------
1377 632043 \ 632043 1377 1377 / 1377 1377
$$x_{1} = - \frac{4433}{1377} - \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right)$$
/ 1 \ / / 1 \ \
34975204*re|-------------------------------------------------------------| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| / / ____________________\\ / / ____________________\\
| ________________________________________| | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||
|/ ___\ / ____________________ | | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| |atan|--------------------------|| |atan|--------------------------||
|| 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | __________ | \ 10758961249 /| _________ | \ 10758961249 /|| _________ | \ 10758961249 /| __________ | \ 10758961249 /|
||- - + -------|*3 / ----------- + ------------------------ | | ||- - + -------|*3 / ----------- + ------------------------ | \/ 26231403 *cos|--------------------------------| \/ 8743801 *sin|--------------------------------|| \/ 8743801 *cos|--------------------------------| \/ 26231403 *sin|--------------------------------|
4433 \\ 2 2 / \/ 193405158 421362 / | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = - ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + ------------------------------------------------- + --------------------------------------------------
1377 632043 \ 632043 1377 1377 / 1377 1377
$$x_{2} = - \frac{4433}{1377} + \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right)$$
________________________________________
/ ____________________
/ 10758961249 I*\/ 811748575929195255
3 / ----------- + ------------------------
4433 34975204 \/ 193405158 421362
x3 = - ---- - ---------------------------------------------------- - ---------------------------------------------
1377 ________________________________________ 3
/ ____________________
/ 10758961249 I*\/ 811748575929195255
632043*3 / ----------- + ------------------------
\/ 193405158 421362
$$x_{3} = - \frac{4433}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}$$
x3 = -4433/1377 - (10758961249/193405158 + sqrt(811748575929195255)*i/421362)^(1/3)/3 - 34975204/(632043*(10758961249/193405158 + sqrt(811748575929195255)*i/421362)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
34975204*re|-------------------------------------------------------------| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| / / ____________________\\ / / ____________________\\ 34975204*re|-------------------------------------------------------------| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| / / ____________________\\ / / ____________________\\
| ________________________________________| | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 || | ________________________________________| | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 || ________________________________________
|/ ___\ / ____________________ | | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| |atan|--------------------------|| |atan|--------------------------|| |/ ___\ / ____________________ | | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| |atan|--------------------------|| |atan|--------------------------|| / ____________________
|| 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | _________ | \ 10758961249 /| __________ | \ 10758961249 /|| __________ | \ 10758961249 /| _________ | \ 10758961249 /| || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | __________ | \ 10758961249 /| _________ | \ 10758961249 /|| _________ | \ 10758961249 /| __________ | \ 10758961249 /| / 10758961249 I*\/ 811748575929195255
||- - - -------|*3 / ----------- + ------------------------ | | ||- - - -------|*3 / ----------- + ------------------------ | \/ 8743801 *sin|--------------------------------| \/ 26231403 *cos|--------------------------------|| \/ 26231403 *sin|--------------------------------| \/ 8743801 *cos|--------------------------------| ||- - + -------|*3 / ----------- + ------------------------ | | ||- - + -------|*3 / ----------- + ------------------------ | \/ 26231403 *cos|--------------------------------| \/ 8743801 *sin|--------------------------------|| \/ 8743801 *cos|--------------------------------| \/ 26231403 *sin|--------------------------------| 3 / ----------- + ------------------------
4433 \\ 2 2 / \/ 193405158 421362 / | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| \ 3 / \ 3 / 4433 \\ 2 2 / \/ 193405158 421362 / | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| \ 3 / \ 3 / 4433 34975204 \/ 193405158 421362
- ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| - -------------------------------------------------- + ------------------------------------------------- + - ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + ------------------------------------------------- + -------------------------------------------------- + - ---- - ---------------------------------------------------- - ---------------------------------------------
1377 632043 \ 632043 1377 1377 / 1377 1377 1377 632043 \ 632043 1377 1377 / 1377 1377 1377 ________________________________________ 3
/ ____________________
/ 10758961249 I*\/ 811748575929195255
632043*3 / ----------- + ------------------------
\/ 193405158 421362
$$\left(\left(- \frac{4433}{1377} - \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right)\right) + \left(- \frac{4433}{1377} + \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right)\right)\right) + \left(- \frac{4433}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
34975204*re|-------------------------------------------------------------| 34975204*re|-------------------------------------------------------------| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| / / ____________________\\
| ________________________________________| | ________________________________________| ________________________________________ | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | |459*\/ 811748575929195255 ||
|/ ___\ / ____________________ | |/ ___\ / ____________________ | / ____________________ | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| |atan|--------------------------||
|| 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | / 10758961249 I*\/ 811748575929195255 | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | __________ | \ 10758961249 /| _________ | \ 10758961249 /|| | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | _________ | \ 10758961249 /| __________ | \ 10758961249 /|| _________ | \ 10758961249 /|
||- - + -------|*3 / ----------- + ------------------------ | ||- - - -------|*3 / ----------- + ------------------------ | 3 / ----------- + ------------------------ | ||- - + -------|*3 / ----------- + ------------------------ | \/ 26231403 *cos|--------------------------------| \/ 8743801 *sin|--------------------------------|| | ||- - - -------|*3 / ----------- + ------------------------ | \/ 8743801 *sin|--------------------------------| \/ 26231403 *cos|--------------------------------|| 2*\/ 8743801 *cos|--------------------------------|
4433 34975204 \\ 2 2 / \/ 193405158 421362 / \\ 2 2 / \/ 193405158 421362 / \/ 193405158 421362 | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| \ 3 /
- ---- - ---------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - --------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| + ---------------------------------------------------
459 ________________________________________ 632043 632043 3 \ 632043 1377 1377 / \ 632043 1377 1377 / 1377
/ ____________________
/ 10758961249 I*\/ 811748575929195255
632043*3 / ----------- + ------------------------
\/ 193405158 421362
$$- \frac{4433}{459} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{2 \sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right) + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right) - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 34975204*re|-------------------------------------------------------------| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| / / ____________________\\ / / ____________________\\| | 34975204*re|-------------------------------------------------------------| | 34975204*im|-------------------------------------------------------------| / / ____________________\\ / / ____________________\\| / / ____________________\\ / / ____________________\\|
| | ________________________________________| | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | | ________________________________________| | | ________________________________________| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 ||| / ________________________________________\
| |/ ___\ / ____________________ | | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| |atan|--------------------------|| |atan|--------------------------||| | |/ ___\ / ____________________ | | |/ ___\ / ____________________ | |atan|--------------------------|| |atan|--------------------------||| |atan|--------------------------|| |atan|--------------------------||| | / ____________________ |
| || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | _________ | \ 10758961249 /| __________ | \ 10758961249 /|| __________ | \ 10758961249 /| _________ | \ 10758961249 /|| | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | | || 1 I*\/ 3 | / 10758961249 I*\/ 811748575929195255 | __________ | \ 10758961249 /| _________ | \ 10758961249 /|| _________ | \ 10758961249 /| __________ | \ 10758961249 /|| | / 10758961249 I*\/ 811748575929195255 |
| ||- - - -------|*3 / ----------- + ------------------------ | | ||- - - -------|*3 / ----------- + ------------------------ | \/ 8743801 *sin|--------------------------------| \/ 26231403 *cos|--------------------------------|| \/ 26231403 *sin|--------------------------------| \/ 8743801 *cos|--------------------------------|| | ||- - + -------|*3 / ----------- + ------------------------ | | ||- - + -------|*3 / ----------- + ------------------------ | \/ 26231403 *cos|--------------------------------| \/ 8743801 *sin|--------------------------------|| \/ 8743801 *cos|--------------------------------| \/ 26231403 *sin|--------------------------------|| | 3 / ----------- + ------------------------ |
| 4433 \\ 2 2 / \/ 193405158 421362 / | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| \ 3 / \ 3 /| | 4433 \\ 2 2 / \/ 193405158 421362 / | \\ 2 2 / \/ 193405158 421362 / \ 3 / \ 3 /| \ 3 / \ 3 /| | 4433 34975204 \/ 193405158 421362 |
|- ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| - -------------------------------------------------- + -------------------------------------------------|*|- ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + ------------------------------------------------- + --------------------------------------------------|*|- ---- - ---------------------------------------------------- - ---------------------------------------------|
\ 1377 632043 \ 632043 1377 1377 / 1377 1377 / \ 1377 632043 \ 632043 1377 1377 / 1377 1377 / | 1377 ________________________________________ 3 |
| / ____________________ |
| / 10758961249 I*\/ 811748575929195255 |
| 632043*3 / ----------- + ------------------------ |
\ \/ 193405158 421362 /
$$\left(- \frac{4433}{1377} - \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right)\right) \left(- \frac{4433}{1377} + \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right)\right) \left(- \frac{4433}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)$$
=
/ / / ____________________\\ / / ____________________\\\
| | |459*\/ 811748575929195255 || | |459*\/ 811748575929195255 |||
/ ____________________________________________ / ____________________________________________\\ | |2*atan|--------------------------|| |atan|--------------------------|||
| 3 ___ 3 / ____________________ | 2/3 3 / ____________________ || | | \ 10758961249 /| _________ | \ 10758961249 /||
\69950408*\/ 2 + \/ 10758961249 + 459*I*\/ 811748575929195255 *\8866 + 2 *\/ 10758961249 + 459*I*\/ 811748575929195255 //*|15323715 - 69950408*cos|----------------------------------| + 17732*\/ 8743801 *cos|--------------------------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
____________________________________________
3 / ____________________
5221939266*\/ 10758961249 + 459*I*\/ 811748575929195255
$$\frac{\left(69950408 \sqrt[3]{2} + \left(8866 + 2^{\frac{2}{3}} \sqrt[3]{10758961249 + 459 \sqrt{811748575929195255} i}\right) \sqrt[3]{10758961249 + 459 \sqrt{811748575929195255} i}\right) \left(- 69950408 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)} + 15323715 + 17732 \sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}\right)}{5221939266 \sqrt[3]{10758961249 + 459 \sqrt{811748575929195255} i}}$$
(69950408*2^(1/3) + (10758961249 + 459*i*sqrt(811748575929195255))^(1/3)*(8866 + 2^(2/3)*(10758961249 + 459*i*sqrt(811748575929195255))^(1/3)))*(15323715 - 69950408*cos(2*atan(459*sqrt(811748575929195255)/10758961249)/3) + 17732*sqrt(8743801)*cos(atan(459*sqrt(811748575929195255)/10758961249)/3))/(5221939266*(10758961249 + 459*i*sqrt(811748575929195255))^(1/3))
Respuesta numérica
[src]
x1 = -10.695141588861
x2 = -3.14484442976019
x3 = 4.18203394890436
x3 = 4.18203394890436