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- 51,03 multiplicar por b al cubo más 401,7 multiplicar por b al cuadrado menos 694 es igual a 0
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Expresiones semejantes
- 51,03*b^3-401,7*b^2-694=0
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51,03*b^3+401,7*b^2-694=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 5103*b 4017*b ------- + ------- - 694 = 0 100 10
$$\left(\frac{5103 b^{3}}{100} + \frac{4017 b^{2}}{10}\right) - 694 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(\frac{5103 b^{3}}{100} + \frac{4017 b^{2}}{10}\right) - 694 = 0$$
de
$$a b^{3} + b^{3} + b c + d = 0$$
como ecuación cúbica reducida
$$b^{3} + \frac{b^{3}}{a} + \frac{b c}{a} + \frac{d}{a} = 0$$
$$b^{3} + \frac{13390 b^{2}}{1701} - \frac{69400}{5103} = 0$$
$$b^{3} + b^{2} p + b q + v = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{13390}{1701}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = - \frac{69400}{5103}$$
Fórmulas de Cardano-Vieta
$$b_{1} + b_{2} + b_{3} = - p$$
$$b_{1} b_{2} + b_{1} b_{3} + b_{2} b_{3} = q$$
$$b_{1} b_{2} b_{3} = v$$
$$b_{1} + b_{2} + b_{3} = - \frac{13390}{1701}$$
$$b_{1} b_{2} + b_{1} b_{3} + b_{2} b_{3} = 0$$
$$b_{1} b_{2} b_{3} = - \frac{69400}{5103}$$
$$\left(\frac{5103 b^{3}}{100} + \frac{4017 b^{2}}{10}\right) - 694 = 0$$
de
$$a b^{3} + b^{3} + b c + d = 0$$
como ecuación cúbica reducida
$$b^{3} + \frac{b^{3}}{a} + \frac{b c}{a} + \frac{d}{a} = 0$$
$$b^{3} + \frac{13390 b^{2}}{1701} - \frac{69400}{5103} = 0$$
$$b^{3} + b^{2} p + b q + v = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{13390}{1701}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = - \frac{69400}{5103}$$
Fórmulas de Cardano-Vieta
$$b_{1} + b_{2} + b_{3} = - p$$
$$b_{1} b_{2} + b_{1} b_{3} + b_{2} b_{3} = q$$
$$b_{1} b_{2} b_{3} = v$$
$$b_{1} + b_{2} + b_{3} = - \frac{13390}{1701}$$
$$b_{1} b_{2} + b_{1} b_{3} + b_{2} b_{3} = 0$$
$$b_{1} b_{2} b_{3} = - \frac{69400}{5103}$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
89646050*re|-------------------------------------------------------------| / / ________________\\ | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\| / / ________________\\
| ________________________________________| | |5103*\/ 13525481570779 || | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 ||| | |5103*\/ 13525481570779 ||
|/ ___\ / ________________ | |atan|-----------------------|| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------||| |atan|-----------------------||
|| 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /|| ___ | \ 14971120867 /|
||- - - -------|*3 / ------------ + ----------------------- | 6695*cos|-----------------------------| | ||- - - -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------|| 6695*\/ 3 *sin|-----------------------------|
13390 \\ 2 2 / \/ 9843350202 1928934 / \ 3 / | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /| \ 3 /
b1 = - ----- - -------------------------------------------------------------------------- + --------------------------------------- + I*|- -------------------------------------------------------------------------- + --------------------------------------- + ---------------------------------------------| - ---------------------------------------------
5103 8680203 5103 \ 8680203 5103 5103 / 5103
$$b_{1} = - \frac{13390}{5103} - \frac{6695 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{6695 \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + i \left(- \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103}\right)$$
/ 1 \ / / 1 \ \
89646050*re|-------------------------------------------------------------| / / ________________\\ | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\| / / ________________\\
| ________________________________________| | |5103*\/ 13525481570779 || | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 ||| | |5103*\/ 13525481570779 ||
|/ ___\ / ________________ | |atan|-----------------------|| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------||| |atan|-----------------------||
|| 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /|| ___ | \ 14971120867 /|
||- - + -------|*3 / ------------ + ----------------------- | 6695*cos|-----------------------------| | ||- - + -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------|| 6695*\/ 3 *sin|-----------------------------|
13390 \\ 2 2 / \/ 9843350202 1928934 / \ 3 / | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /| \ 3 /
b2 = - ----- - -------------------------------------------------------------------------- + --------------------------------------- + I*|- -------------------------------------------------------------------------- + --------------------------------------- - ---------------------------------------------| + ---------------------------------------------
5103 8680203 5103 \ 8680203 5103 5103 / 5103
$$b_{2} = - \frac{13390}{5103} + \frac{6695 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + i \left(- \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203}\right)$$
________________________________________
/ ________________
/ 374278021675 25*I*\/ 13525481570779
2*3 / ------------ + -----------------------
13390 89646050 \/ 9843350202 1928934
b3 = - ----- - ----------------------------------------------------- - -----------------------------------------------
5103 ________________________________________ 3
/ ________________
/ 374278021675 25*I*\/ 13525481570779
8680203*3 / ------------ + -----------------------
\/ 9843350202 1928934
$$b_{3} = - \frac{13390}{5103} - \frac{2 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}{3} - \frac{89646050}{8680203 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}$$
b3 = -13390/5103 - 2*(374278021675/9843350202 + 25*sqrt(13525481570779)*i/1928934)^(1/3)/3 - 89646050/(8680203*(374278021675/9843350202 + 25*sqrt(13525481570779)*i/1928934)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
89646050*re|-------------------------------------------------------------| / / ________________\\ | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\| / / ________________\\ 89646050*re|-------------------------------------------------------------| / / ________________\\ | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\| / / ________________\\
| ________________________________________| | |5103*\/ 13525481570779 || | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 ||| | |5103*\/ 13525481570779 || | ________________________________________| | |5103*\/ 13525481570779 || | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 ||| | |5103*\/ 13525481570779 || ________________________________________
|/ ___\ / ________________ | |atan|-----------------------|| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------||| |atan|-----------------------|| |/ ___\ / ________________ | |atan|-----------------------|| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------||| |atan|-----------------------|| / ________________
|| 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /|| ___ | \ 14971120867 /| || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /|| ___ | \ 14971120867 /| / 374278021675 25*I*\/ 13525481570779
||- - - -------|*3 / ------------ + ----------------------- | 6695*cos|-----------------------------| | ||- - - -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------|| 6695*\/ 3 *sin|-----------------------------| ||- - + -------|*3 / ------------ + ----------------------- | 6695*cos|-----------------------------| | ||- - + -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------|| 6695*\/ 3 *sin|-----------------------------| 2*3 / ------------ + -----------------------
13390 \\ 2 2 / \/ 9843350202 1928934 / \ 3 / | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /| \ 3 / 13390 \\ 2 2 / \/ 9843350202 1928934 / \ 3 / | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /| \ 3 / 13390 89646050 \/ 9843350202 1928934
- ----- - -------------------------------------------------------------------------- + --------------------------------------- + I*|- -------------------------------------------------------------------------- + --------------------------------------- + ---------------------------------------------| - --------------------------------------------- + - ----- - -------------------------------------------------------------------------- + --------------------------------------- + I*|- -------------------------------------------------------------------------- + --------------------------------------- - ---------------------------------------------| + --------------------------------------------- + - ----- - ----------------------------------------------------- - -----------------------------------------------
5103 8680203 5103 \ 8680203 5103 5103 / 5103 5103 8680203 5103 \ 8680203 5103 5103 / 5103 5103 ________________________________________ 3
/ ________________
/ 374278021675 25*I*\/ 13525481570779
8680203*3 / ------------ + -----------------------
\/ 9843350202 1928934
$$\left(\left(- \frac{13390}{5103} + \frac{6695 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + i \left(- \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203}\right)\right) + \left(- \frac{13390}{5103} - \frac{6695 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{6695 \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + i \left(- \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103}\right)\right)\right) + \left(- \frac{13390}{5103} - \frac{2 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}{3} - \frac{89646050}{8680203 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
89646050*re|-------------------------------------------------------------| 89646050*re|-------------------------------------------------------------| / / ________________\\ | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\| | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\|
| ________________________________________| | ________________________________________| ________________________________________ | |5103*\/ 13525481570779 || | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 ||| | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 |||
|/ ___\ / ________________ | |/ ___\ / ________________ | / ________________ |atan|-----------------------|| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------||| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------|||
|| 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | / 374278021675 25*I*\/ 13525481570779 | \ 14971120867 /| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /|| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /||
||- - + -------|*3 / ------------ + ----------------------- | ||- - - -------|*3 / ------------ + ----------------------- | 2*3 / ------------ + ----------------------- 13390*cos|-----------------------------| | ||- - + -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------|| | ||- - - -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------||
13390 89646050 \\ 2 2 / \/ 9843350202 1928934 / \\ 2 2 / \/ 9843350202 1928934 / \/ 9843350202 1928934 \ 3 / | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /| | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /|
- ----- - ----------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - ----------------------------------------------- + ---------------------------------------- + I*|- -------------------------------------------------------------------------- + --------------------------------------- - ---------------------------------------------| + I*|- -------------------------------------------------------------------------- + --------------------------------------- + ---------------------------------------------|
1701 ________________________________________ 8680203 8680203 3 5103 \ 8680203 5103 5103 / \ 8680203 5103 5103 /
/ ________________
/ 374278021675 25*I*\/ 13525481570779
8680203*3 / ------------ + -----------------------
\/ 9843350202 1928934
$$- \frac{13390}{1701} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{13390 \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{2 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}{3} + i \left(- \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203}\right) + i \left(- \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103}\right) - \frac{89646050}{8680203 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 89646050*re|-------------------------------------------------------------| / / ________________\\ | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\| / / ________________\\| | 89646050*re|-------------------------------------------------------------| / / ________________\\ | 89646050*im|-------------------------------------------------------------| / / ________________\\ / / ________________\\| / / ________________\\|
| | ________________________________________| | |5103*\/ 13525481570779 || | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 ||| | |5103*\/ 13525481570779 ||| | | ________________________________________| | |5103*\/ 13525481570779 || | | ________________________________________| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 ||| | |5103*\/ 13525481570779 ||| / ________________________________________\
| |/ ___\ / ________________ | |atan|-----------------------|| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------||| |atan|-----------------------||| | |/ ___\ / ________________ | |atan|-----------------------|| | |/ ___\ / ________________ | |atan|-----------------------|| |atan|-----------------------||| |atan|-----------------------||| | / ________________ |
| || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /|| ___ | \ 14971120867 /|| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| | || 1 I*\/ 3 | / 374278021675 25*I*\/ 13525481570779 | | \ 14971120867 /| ___ | \ 14971120867 /|| ___ | \ 14971120867 /|| | / 374278021675 25*I*\/ 13525481570779 |
| ||- - - -------|*3 / ------------ + ----------------------- | 6695*cos|-----------------------------| | ||- - - -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------|| 6695*\/ 3 *sin|-----------------------------|| | ||- - + -------|*3 / ------------ + ----------------------- | 6695*cos|-----------------------------| | ||- - + -------|*3 / ------------ + ----------------------- | 6695*sin|-----------------------------| 6695*\/ 3 *cos|-----------------------------|| 6695*\/ 3 *sin|-----------------------------|| | 2*3 / ------------ + ----------------------- |
| 13390 \\ 2 2 / \/ 9843350202 1928934 / \ 3 / | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /| \ 3 /| | 13390 \\ 2 2 / \/ 9843350202 1928934 / \ 3 / | \\ 2 2 / \/ 9843350202 1928934 / \ 3 / \ 3 /| \ 3 /| | 13390 89646050 \/ 9843350202 1928934 |
|- ----- - -------------------------------------------------------------------------- + --------------------------------------- + I*|- -------------------------------------------------------------------------- + --------------------------------------- + ---------------------------------------------| - ---------------------------------------------|*|- ----- - -------------------------------------------------------------------------- + --------------------------------------- + I*|- -------------------------------------------------------------------------- + --------------------------------------- - ---------------------------------------------| + ---------------------------------------------|*|- ----- - ----------------------------------------------------- - -----------------------------------------------|
\ 5103 8680203 5103 \ 8680203 5103 5103 / 5103 / \ 5103 8680203 5103 \ 8680203 5103 5103 / 5103 / | 5103 ________________________________________ 3 |
| / ________________ |
| / 374278021675 25*I*\/ 13525481570779 |
| 8680203*3 / ------------ + ----------------------- |
\ \/ 9843350202 1928934 /
$$\left(- \frac{13390}{5103} - \frac{6695 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{6695 \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + i \left(- \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103}\right)\right) \left(- \frac{13390}{5103} + \frac{6695 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203} + i \left(- \frac{6695 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} + \frac{6695 \sin{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}}{5103} - \frac{89646050 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)}}{8680203}\right)\right) \left(- \frac{13390}{5103} - \frac{2 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}{3} - \frac{89646050}{8680203 \sqrt[3]{\frac{374278021675}{9843350202} + \frac{25 \sqrt{13525481570779} i}{1928934}}}\right)$$
=
/ / / ________________\\ / / ________________\\\
| | |5103*\/ 13525481570779 || | |5103*\/ 13525481570779 |||
| |2*atan|-----------------------|| |atan|-----------------------||| / _________________________________________ / _________________________________________\\
3 ___ | | \ 14971120867 /| | \ 14971120867 /|| | 3 ___ 2/3 3 / ________________ | 2/3 3 / ________________ ||
71716840*\/ 5 *|- cos|-------------------------------| + cos|-----------------------------||*\89646050*\/ 2 + 5 *\/ 14971120867 + 5103*I*\/ 13525481570779 *\13390 + 10 *\/ 14971120867 + 5103*I*\/ 13525481570779 //
\ \ 3 / \ 3 //
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_________________________________________
3 / ________________
132885227727*\/ 14971120867 + 5103*I*\/ 13525481570779
$$\frac{71716840 \sqrt[3]{5} \left(89646050 \sqrt[3]{2} + 5^{\frac{2}{3}} \left(13390 + 10^{\frac{2}{3}} \sqrt[3]{14971120867 + 5103 \sqrt{13525481570779} i}\right) \sqrt[3]{14971120867 + 5103 \sqrt{13525481570779} i}\right) \left(- \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{5103 \sqrt{13525481570779}}{14971120867} \right)}}{3} \right)}\right)}{132885227727 \sqrt[3]{14971120867 + 5103 \sqrt{13525481570779} i}}$$
71716840*5^(1/3)*(-cos(2*atan(5103*sqrt(13525481570779)/14971120867)/3) + cos(atan(5103*sqrt(13525481570779)/14971120867)/3))*(89646050*2^(1/3) + 5^(2/3)*(14971120867 + 5103*i*sqrt(13525481570779))^(1/3)*(13390 + 10^(2/3)*(14971120867 + 5103*i*sqrt(13525481570779))^(1/3)))/(132885227727*(14971120867 + 5103*i*sqrt(13525481570779))^(1/3))
Respuesta numérica
[src]
b1 = 1.22284950067638
b2 = -1.45591987082994
b3 = -7.63876972390876
b3 = -7.63876972390876