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Expresiones idénticas
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- 53,72 multiplicar por (x al cubo ) más 412,667 multiplicar por (x al cuadrado ) menos 438,8 es igual a 0
- cincuenta y tres , setenta y dos multiplicar por (x en el grado tres) más cuatrocientos doce , seiscientos sesenta y siete multiplicar por (x en el grado dos) menos cuatrocientos treinta y ocho , ocho es igual a cero
- 53,72*(x3)+412,667*(x2)-438,8=0
- 53,72*x3+412,667*x2-438,8=0
- 53,72*(x³)+412,667*(x²)-438,8=0
- 53,72*(x en el grado 3)+412,667*(x en el grado 2)-438,8=0
- 53,72(x^3)+412,667(x^2)-438,8=0
- 53,72(x3)+412,667(x2)-438,8=0
- 53,72x3+412,667x2-438,8=0
- 53,72x^3+412,667x^2-438,8=0
- 53,72*(x^3)+412,667*(x^2)-438,8=O
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Expresiones semejantes
- 53,72*(x^3)+412,667*(x^2)+438,8=0
- 53,72*(x^3)-412,667*(x^2)-438,8=0
53,72*(x^3)+412,667*(x^2)-438,8=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 1343*x 412667*x 2194 ------- + --------- - ---- = 0 25 1000 5
$$\left(\frac{1343 x^{3}}{25} + \frac{412667 x^{2}}{1000}\right) - \frac{2194}{5} = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(\frac{1343 x^{3}}{25} + \frac{412667 x^{2}}{1000}\right) - \frac{2194}{5} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{412667 x^{2}}{53720} - \frac{10970}{1343} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{412667}{53720}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = - \frac{10970}{1343}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{412667}{53720}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = - \frac{10970}{1343}$$
$$\left(\frac{1343 x^{3}}{25} + \frac{412667 x^{2}}{1000}\right) - \frac{2194}{5} = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} + \frac{412667 x^{2}}{53720} - \frac{10970}{1343} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{412667}{53720}$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = - \frac{10970}{1343}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = - \frac{412667}{53720}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = - \frac{10970}{1343}$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
170294052889*re|------------------------------------------------------------------------| / / _______________________\\ | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\| / / _______________________\\
| ___________________________________________________| | |3223200*\/ 203144120309231113233 || | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 ||| | |3223200*\/ 203144120309231113233 ||
|/ ___\ / _______________________ | |atan|---------------------------------|| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------||| |atan|---------------------------------||
|| 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /|| ___ | \ 53179606409624963 /|
||- - - -------|*3 / ----------------- + ----------------------------- | 412667*cos|---------------------------------------| | ||- - - -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------|| 412667*\/ 3 *sin|---------------------------------------|
412667 \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /| \ 3 /
x1 = - ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------| - ---------------------------------------------------------
161160 8657515200 322320 \ 8657515200 322320 322320 / 322320
$$x_{1} = - \frac{412667}{161160} - \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right)$$
/ 1 \ / / 1 \ \
170294052889*re|------------------------------------------------------------------------| / / _______________________\\ | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\| / / _______________________\\
| ___________________________________________________| | |3223200*\/ 203144120309231113233 || | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 ||| | |3223200*\/ 203144120309231113233 ||
|/ ___\ / _______________________ | |atan|---------------------------------|| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------||| |atan|---------------------------------||
|| 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /|| ___ | \ 53179606409624963 /|
||- - + -------|*3 / ----------------- + ----------------------------- | 412667*cos|---------------------------------------| | ||- - + -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------|| 412667*\/ 3 *sin|---------------------------------------|
412667 \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /| \ 3 /
x2 = - ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + ---------------------------------------------------------
161160 8657515200 322320 \ 8657515200 322320 322320 / 322320
$$x_{2} = - \frac{412667}{161160} + \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right)$$
___________________________________________________
/ _______________________
/ 53179606409624963 3*I*\/ 203144120309231113233
3 / ----------------- + -----------------------------
412667 170294052889 \/ 155027238848000 144291920
x3 = - ------ - ------------------------------------------------------------------- - --------------------------------------------------------
161160 ___________________________________________________ 3
/ _______________________
/ 53179606409624963 3*I*\/ 203144120309231113233
8657515200*3 / ----------------- + -----------------------------
\/ 155027238848000 144291920
$$x_{3} = - \frac{412667}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}$$
x3 = -412667/161160 - (53179606409624963/155027238848000 + 3*sqrt(203144120309231113233)*i/144291920)^(1/3)/3 - 170294052889/(8657515200*(53179606409624963/155027238848000 + 3*sqrt(203144120309231113233)*i/144291920)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
170294052889*re|------------------------------------------------------------------------| / / _______________________\\ | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\| / / _______________________\\ 170294052889*re|------------------------------------------------------------------------| / / _______________________\\ | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\| / / _______________________\\
| ___________________________________________________| | |3223200*\/ 203144120309231113233 || | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 ||| | |3223200*\/ 203144120309231113233 || | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 ||| | |3223200*\/ 203144120309231113233 || ___________________________________________________
|/ ___\ / _______________________ | |atan|---------------------------------|| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------||| |atan|---------------------------------|| |/ ___\ / _______________________ | |atan|---------------------------------|| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------||| |atan|---------------------------------|| / _______________________
|| 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /|| ___ | \ 53179606409624963 /| || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /|| ___ | \ 53179606409624963 /| / 53179606409624963 3*I*\/ 203144120309231113233
||- - - -------|*3 / ----------------- + ----------------------------- | 412667*cos|---------------------------------------| | ||- - - -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------|| 412667*\/ 3 *sin|---------------------------------------| ||- - + -------|*3 / ----------------- + ----------------------------- | 412667*cos|---------------------------------------| | ||- - + -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------|| 412667*\/ 3 *sin|---------------------------------------| 3 / ----------------- + -----------------------------
412667 \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /| \ 3 / 412667 \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /| \ 3 / 412667 170294052889 \/ 155027238848000 144291920
- ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------| - --------------------------------------------------------- + - ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + --------------------------------------------------------- + - ------ - ------------------------------------------------------------------- - --------------------------------------------------------
161160 8657515200 322320 \ 8657515200 322320 322320 / 322320 161160 8657515200 322320 \ 8657515200 322320 322320 / 322320 161160 ___________________________________________________ 3
/ _______________________
/ 53179606409624963 3*I*\/ 203144120309231113233
8657515200*3 / ----------------- + -----------------------------
\/ 155027238848000 144291920
$$\left(\left(- \frac{412667}{161160} - \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right)\right) + \left(- \frac{412667}{161160} + \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right)\right)\right) + \left(- \frac{412667}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
170294052889*re|------------------------------------------------------------------------| 170294052889*re|------------------------------------------------------------------------| / / _______________________\\ | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\| | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\|
| ___________________________________________________| | ___________________________________________________| ___________________________________________________ | |3223200*\/ 203144120309231113233 || | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 ||| | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 |||
|/ ___\ / _______________________ | |/ ___\ / _______________________ | / _______________________ |atan|---------------------------------|| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------||| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------|||
|| 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | / 53179606409624963 3*I*\/ 203144120309231113233 | \ 53179606409624963 /| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /|| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /||
||- - + -------|*3 / ----------------- + ----------------------------- | ||- - - -------|*3 / ----------------- + ----------------------------- | 3 / ----------------- + ----------------------------- 412667*cos|---------------------------------------| | ||- - + -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------|| | ||- - - -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------||
412667 170294052889 \\ 2 2 / \/ 155027238848000 144291920 / \\ 2 2 / \/ 155027238848000 144291920 / \/ 155027238848000 144291920 \ 3 / | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /| | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /|
- ------ - ------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - -------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------|
53720 ___________________________________________________ 8657515200 8657515200 3 161160 \ 8657515200 322320 322320 / \ 8657515200 322320 322320 /
/ _______________________
/ 53179606409624963 3*I*\/ 203144120309231113233
8657515200*3 / ----------------- + -----------------------------
\/ 155027238848000 144291920
$$- \frac{412667}{53720} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right) + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right) - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 170294052889*re|------------------------------------------------------------------------| / / _______________________\\ | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\| / / _______________________\\| | 170294052889*re|------------------------------------------------------------------------| / / _______________________\\ | 170294052889*im|------------------------------------------------------------------------| / / _______________________\\ / / _______________________\\| / / _______________________\\|
| | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 ||| | |3223200*\/ 203144120309231113233 ||| | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | | ___________________________________________________| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 ||| | |3223200*\/ 203144120309231113233 ||| / ___________________________________________________\
| |/ ___\ / _______________________ | |atan|---------------------------------|| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------||| |atan|---------------------------------||| | |/ ___\ / _______________________ | |atan|---------------------------------|| | |/ ___\ / _______________________ | |atan|---------------------------------|| |atan|---------------------------------||| |atan|---------------------------------||| | / _______________________ |
| || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /|| ___ | \ 53179606409624963 /|| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| | || 1 I*\/ 3 | / 53179606409624963 3*I*\/ 203144120309231113233 | | \ 53179606409624963 /| ___ | \ 53179606409624963 /|| ___ | \ 53179606409624963 /|| | / 53179606409624963 3*I*\/ 203144120309231113233 |
| ||- - - -------|*3 / ----------------- + ----------------------------- | 412667*cos|---------------------------------------| | ||- - - -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------|| 412667*\/ 3 *sin|---------------------------------------|| | ||- - + -------|*3 / ----------------- + ----------------------------- | 412667*cos|---------------------------------------| | ||- - + -------|*3 / ----------------- + ----------------------------- | 412667*sin|---------------------------------------| 412667*\/ 3 *cos|---------------------------------------|| 412667*\/ 3 *sin|---------------------------------------|| | 3 / ----------------- + ----------------------------- |
| 412667 \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /| \ 3 /| | 412667 \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / | \\ 2 2 / \/ 155027238848000 144291920 / \ 3 / \ 3 /| \ 3 /| | 412667 170294052889 \/ 155027238848000 144291920 |
|- ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------| - ---------------------------------------------------------|*|- ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + ---------------------------------------------------------|*|- ------ - ------------------------------------------------------------------- - --------------------------------------------------------|
\ 161160 8657515200 322320 \ 8657515200 322320 322320 / 322320 / \ 161160 8657515200 322320 \ 8657515200 322320 322320 / 322320 / | 161160 ___________________________________________________ 3 |
| / _______________________ |
| / 53179606409624963 3*I*\/ 203144120309231113233 |
| 8657515200*3 / ----------------- + ----------------------------- |
\ \/ 155027238848000 144291920 /
$$\left(- \frac{412667}{161160} - \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right)\right) \left(- \frac{412667}{161160} + \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right)\right) \left(- \frac{412667}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)$$
=
/ / / _______________________\\ / / _______________________\\\
| | |3223200*\/ 203144120309231113233 || | |3223200*\/ 203144120309231113233 |||
/ _________________________________________________________ / _________________________________________________________\\ | |2*atan|---------------------------------|| |atan|---------------------------------|||
| 3 / _______________________ | 3 / _______________________ || | | \ 53179606409624963 /| | \ 53179606409624963 /||
170294052889*\170294052889 + \/ 53179606409624963 + 3223200*I*\/ 203144120309231113233 *\412667 + \/ 53179606409624963 + 3223200*I*\/ 203144120309231113233 //*|- cos|-----------------------------------------| + cos|---------------------------------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_________________________________________________________
3 / _______________________
2092867724448000*\/ 53179606409624963 + 3223200*I*\/ 203144120309231113233
$$\frac{170294052889 \left(170294052889 + \left(412667 + \sqrt[3]{53179606409624963 + 3223200 \sqrt{203144120309231113233} i}\right) \sqrt[3]{53179606409624963 + 3223200 \sqrt{203144120309231113233} i}\right) \left(- \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}\right)}{2092867724448000 \sqrt[3]{53179606409624963 + 3223200 \sqrt{203144120309231113233} i}}$$
170294052889*(170294052889 + (53179606409624963 + 3223200*i*sqrt(203144120309231113233))^(1/3)*(412667 + (53179606409624963 + 3223200*i*sqrt(203144120309231113233))^(1/3)))*(-cos(2*atan(3223200*sqrt(203144120309231113233)/53179606409624963)/3) + cos(atan(3223200*sqrt(203144120309231113233)/53179606409624963)/3))/(2092867724448000*(53179606409624963 + 3223200*i*sqrt(203144120309231113233))^(1/3))
Respuesta numérica
[src]
x1 = -1.1153173930661
x2 = 0.971566283654639
x3 = -7.53806199557737
x3 = -7.53806199557737