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Expresiones idénticas
- 5 cero x^ tres -1185x^ dos +4614x+ mil novecientos cincuenta y tres =0
- 50x al cubo menos 1185x al cuadrado más 4614x más 1953 es igual a 0
- 5 cero x en el grado tres menos 1185x en el grado dos más 4614x más mil novecientos cincuenta y tres es igual a 0
- 50x3-1185x2+4614x+1953=0
- 50x³-1185x²+4614x+1953=0
- 50x en el grado 3-1185x en el grado 2+4614x+1953=0
- 50x^3-1185x^2+4614x+1953=O
-
Expresiones semejantes
- 50x^3+1185x^2+4614x+1953=0
- 50x^3-1185x^2+4614x-1953=0
- 50x^3-1185x^2-4614x+1953=0
50x^3-1185x^2+4614x+1953=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 50*x - 1185*x + 4614*x + 1953 = 0
$$\left(4614 x + \left(50 x^{3} - 1185 x^{2}\right)\right) + 1953 = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(4614 x + \left(50 x^{3} - 1185 x^{2}\right)\right) + 1953 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{237 x^{2}}{10} + \frac{2307 x}{25} + \frac{1953}{50} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{237}{10}$$
$$q = \frac{c}{a}$$
$$q = \frac{2307}{25}$$
$$v = \frac{d}{a}$$
$$v = \frac{1953}{50}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{237}{10}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{2307}{25}$$
$$x_{1} x_{2} x_{3} = \frac{1953}{50}$$
$$\left(4614 x + \left(50 x^{3} - 1185 x^{2}\right)\right) + 1953 = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{237 x^{2}}{10} + \frac{2307 x}{25} + \frac{1953}{50} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{237}{10}$$
$$q = \frac{c}{a}$$
$$q = \frac{2307}{25}$$
$$v = \frac{d}{a}$$
$$v = \frac{1953}{50}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{237}{10}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{2307}{25}$$
$$x_{1} x_{2} x_{3} = \frac{1953}{50}$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
633*re|------------------------------------------------| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| / / ____________\\ / / ____________\\
| ___________________________| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||
|/ ___\ / ____________ | | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| |atan|----------------|| |atan|----------------||
|| 1 I*\/ 3 | / 109003 I*\/ 4955715779 | | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| ______ | \ 109003 /| ______ | \ 109003 /|
||- - - -------|*3 / ------ + ---------------- | | ||- - - -------|*3 / ------ + ---------------- | 3*\/ 1055 *cos|----------------------| \/ 3165 *sin|----------------------|| \/ 3165 *cos|----------------------| 3*\/ 1055 *sin|----------------------|
79 \\ 2 2 / \/ 1000 500 / | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -- + -------------------------------------------------------- + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------ + --------------------------------------
10 20 \ 20 20 20 / 20 20
$$x_{1} = - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right)$$
/ 1 \ / / 1 \ \
633*re|------------------------------------------------| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| / / ____________\\ / / ____________\\
| ___________________________| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||
|/ ___\ / ____________ | | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| |atan|----------------|| |atan|----------------||
|| 1 I*\/ 3 | / 109003 I*\/ 4955715779 | | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| ______ | \ 109003 /| ______ | \ 109003 /|
||- - + -------|*3 / ------ + ---------------- | | ||- - + -------|*3 / ------ + ---------------- | \/ 3165 *sin|----------------------| 3*\/ 1055 *cos|----------------------|| 3*\/ 1055 *sin|----------------------| \/ 3165 *cos|----------------------|
79 \\ 2 2 / \/ 1000 500 / | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| - -------------------------------------- - ------------------------------------
10 20 \ 20 20 20 / 20 20
$$x_{2} = \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right)$$
___________________________
/ ____________
79 / 109003 I*\/ 4955715779 633
x3 = -- + 3 / ------ + ---------------- + -----------------------------------
10 \/ 1000 500 ___________________________
/ ____________
/ 109003 I*\/ 4955715779
20*3 / ------ + ----------------
\/ 1000 500
$$x_{3} = \frac{79}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}$$
x3 = 79/10 + 633/(20*(109003/1000 + sqrt(4955715779)*i/500)^(1/3)) + (109003/1000 + sqrt(4955715779)*i/500)^(1/3)
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
633*re|------------------------------------------------| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| / / ____________\\ / / ____________\\ 633*re|------------------------------------------------| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| / / ____________\\ / / ____________\\
| ___________________________| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | |2*\/ 4955715779 || | |2*\/ 4955715779 || | ___________________________| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||
|/ ___\ / ____________ | | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| |atan|----------------|| |atan|----------------|| |/ ___\ / ____________ | | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| |atan|----------------|| |atan|----------------||
|| 1 I*\/ 3 | / 109003 I*\/ 4955715779 | | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| ______ | \ 109003 /| ______ | \ 109003 /| || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| ______ | \ 109003 /| ______ | \ 109003 /| ___________________________
||- - - -------|*3 / ------ + ---------------- | | ||- - - -------|*3 / ------ + ---------------- | 3*\/ 1055 *cos|----------------------| \/ 3165 *sin|----------------------|| \/ 3165 *cos|----------------------| 3*\/ 1055 *sin|----------------------| ||- - + -------|*3 / ------ + ---------------- | | ||- - + -------|*3 / ------ + ---------------- | \/ 3165 *sin|----------------------| 3*\/ 1055 *cos|----------------------|| 3*\/ 1055 *sin|----------------------| \/ 3165 *cos|----------------------| / ____________
79 \\ 2 2 / \/ 1000 500 / | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| \ 3 / \ 3 / 79 \\ 2 2 / \/ 1000 500 / | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| \ 3 / \ 3 / 79 / 109003 I*\/ 4955715779 633
-- + -------------------------------------------------------- + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------ + -------------------------------------- + -- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| - -------------------------------------- - ------------------------------------ + -- + 3 / ------ + ---------------- + -----------------------------------
10 20 \ 20 20 20 / 20 20 10 20 \ 20 20 20 / 20 20 10 \/ 1000 500 ___________________________
/ ____________
/ 109003 I*\/ 4955715779
20*3 / ------ + ----------------
\/ 1000 500
$$\left(\frac{79}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}\right) + \left(\left(- \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right)\right) + \left(\frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
633*re|------------------------------------------------| 633*re|------------------------------------------------| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| / / ____________\\
| ___________________________| | ___________________________| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | |2*\/ 4955715779 ||
|/ ___\ / ____________ | |/ ___\ / ____________ | | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| |atan|----------------||
___________________________ || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| ______ | \ 109003 /|
/ ____________ ||- - + -------|*3 / ------ + ---------------- | ||- - - -------|*3 / ------ + ---------------- | | ||- - + -------|*3 / ------ + ---------------- | \/ 3165 *sin|----------------------| 3*\/ 1055 *cos|----------------------|| | ||- - - -------|*3 / ------ + ---------------- | 3*\/ 1055 *cos|----------------------| \/ 3165 *sin|----------------------|| \/ 3165 *cos|----------------------|
237 / 109003 I*\/ 4955715779 633 \\ 2 2 / \/ 1000 500 / \\ 2 2 / \/ 1000 500 / | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| \ 3 /
--- + 3 / ------ + ---------------- + ----------------------------------- + -------------------------------------------------------- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------
10 \/ 1000 500 ___________________________ 20 20 \ 20 20 20 / \ 20 20 20 / 10
/ ____________
/ 109003 I*\/ 4955715779
20*3 / ------ + ----------------
\/ 1000 500
$$- \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{10} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{237}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right) + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right) + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 633*re|------------------------------------------------| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| / / ____________\\ / / ____________\\| | 633*re|------------------------------------------------| |633*im|------------------------------------------------| / / ____________\\ / / ____________\\| / / ____________\\ / / ____________\\|
| | ___________________________| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | | ___________________________| | | ___________________________| | |2*\/ 4955715779 || | |2*\/ 4955715779 ||| | |2*\/ 4955715779 || | |2*\/ 4955715779 |||
| |/ ___\ / ____________ | | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| |atan|----------------|| |atan|----------------||| | |/ ___\ / ____________ | | |/ ___\ / ____________ | |atan|----------------|| |atan|----------------||| |atan|----------------|| |atan|----------------|||
| || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| ______ | \ 109003 /| ______ | \ 109003 /|| | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | | || 1 I*\/ 3 | / 109003 I*\/ 4955715779 | ______ | \ 109003 /| ______ | \ 109003 /|| ______ | \ 109003 /| ______ | \ 109003 /|| / ___________________________ \
| ||- - - -------|*3 / ------ + ---------------- | | ||- - - -------|*3 / ------ + ---------------- | 3*\/ 1055 *cos|----------------------| \/ 3165 *sin|----------------------|| \/ 3165 *cos|----------------------| 3*\/ 1055 *sin|----------------------|| | ||- - + -------|*3 / ------ + ---------------- | | ||- - + -------|*3 / ------ + ---------------- | \/ 3165 *sin|----------------------| 3*\/ 1055 *cos|----------------------|| 3*\/ 1055 *sin|----------------------| \/ 3165 *cos|----------------------|| | / ____________ |
|79 \\ 2 2 / \/ 1000 500 / | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| \ 3 / \ 3 /| |79 \\ 2 2 / \/ 1000 500 / | \\ 2 2 / \/ 1000 500 / \ 3 / \ 3 /| \ 3 / \ 3 /| |79 / 109003 I*\/ 4955715779 633 |
|-- + -------------------------------------------------------- + I*|-------------------------------------------------------- - -------------------------------------- - ------------------------------------| - ------------------------------------ + --------------------------------------|*|-- + -------------------------------------------------------- + I*|-------------------------------------------------------- - ------------------------------------ + --------------------------------------| - -------------------------------------- - ------------------------------------|*|-- + 3 / ------ + ---------------- + -----------------------------------|
\10 20 \ 20 20 20 / 20 20 / \10 20 \ 20 20 20 / 20 20 / |10 \/ 1000 500 ___________________________|
| / ____________ |
| / 109003 I*\/ 4955715779 |
| 20*3 / ------ + ---------------- |
\ \/ 1000 500 /
$$\left(- \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} + \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(- \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20}\right)\right) \left(\frac{633 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} - \frac{3 \sqrt{1055} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{79}{10} + i \left(\frac{633 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}}\right)}}{20} - \frac{\sqrt{3165} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20} + \frac{3 \sqrt{1055} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}}{20}\right)\right) \left(\frac{79}{10} + \frac{633}{20 \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}} + \sqrt[3]{\frac{109003}{1000} + \frac{\sqrt{4955715779} i}{500}}\right)$$
=
/ / / ____________\\ / / ____________\\\
| | |2*\/ 4955715779 || | |2*\/ 4955715779 |||
/ _____________________________ / _____________________________\\ | |2*atan|----------------|| |atan|----------------|||
| 3 / ____________ | 3 / ____________ || | | \ 109003 /| ______ | \ 109003 /||
\3165 + \/ 109003 + 2*I*\/ 4955715779 *\79 + \/ 109003 + 2*I*\/ 4955715779 //*|12304 + 25320*cos|------------------------| - 632*\/ 3165 *cos|----------------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_____________________________
3 / ____________
4000*\/ 109003 + 2*I*\/ 4955715779
$$\frac{\left(3165 + \left(79 + \sqrt[3]{109003 + 2 \sqrt{4955715779} i}\right) \sqrt[3]{109003 + 2 \sqrt{4955715779} i}\right) \left(- 632 \sqrt{3165} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)} + 12304 + 25320 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{2 \sqrt{4955715779}}{109003} \right)}}{3} \right)}\right)}{4000 \sqrt[3]{109003 + 2 \sqrt{4955715779} i}}$$
(3165 + (109003 + 2*i*sqrt(4955715779))^(1/3)*(79 + (109003 + 2*i*sqrt(4955715779))^(1/3)))*(12304 + 25320*cos(2*atan(2*sqrt(4955715779)/109003)/3) - 632*sqrt(3165)*cos(atan(2*sqrt(4955715779)/109003)/3))/(4000*(109003 + 2*i*sqrt(4955715779))^(1/3))
Respuesta numérica
[src]
x1 = 18.6357593234578
x2 = -0.384659360573435
x3 = 5.44890003711563
x3 = 5.44890003711563