Sr Examen
-107+1,4*x^2-2,4*(x-6)^2+13,86*(x-9)-0,127*(x-9)^3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 3
7*x 12*(x - 6) 693*(x - 9) 127*(x - 9)
-107 + ---- - ----------- + ----------- - ------------ = 0
5 5 50 1000
$$- \frac{127 \left(x - 9\right)^{3}}{1000} + \left(\frac{693 \left(x - 9\right)}{50} + \left(- \frac{12 \left(x - 6\right)^{2}}{5} + \left(\frac{7 x^{2}}{5} - 107\right)\right)\right) = 0$$
Respuesta rápida
[src]
/ 1 \ / / 1 \ \
10395460*re|------------------------------------------------------------| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| / / _______________\\ / / _______________\\
| _______________________________________| | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||
|/ ___\ / _______________ | | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| |atan|---------------------|| |atan|---------------------||
|| 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| _________ | \ 460071520 /| _________ | \ 460071520 /|
||- - - -------|*3 / ----------- + ----------------------- | | ||- - - -------|*3 / ----------- + ----------------------- | \/ 2598865 *sin|---------------------------| \/ 7796595 *cos|---------------------------|| \/ 7796595 *sin|---------------------------| \/ 2598865 *cos|---------------------------|
2429 \\ 2 2 / \/ 2048383 16129 / | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = ---- - ------------------------------------------------------------------------- + I*|- ------------------------------------------------------------------------- + -------------------------------------------- + --------------------------------------------| - -------------------------------------------- + --------------------------------------------
381 48387 \ 48387 381 381 / 381 381
$$x_{1} = - \frac{\sqrt{7796595} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} - \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{\sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{2429}{381} + i \left(- \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381}\right)$$
/ 1 \ / / 1 \ \
10395460*re|------------------------------------------------------------| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| / / _______________\\ / / _______________\\
| _______________________________________| | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||
|/ ___\ / _______________ | | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| |atan|---------------------|| |atan|---------------------||
|| 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| _________ | \ 460071520 /| _________ | \ 460071520 /|
||- - + -------|*3 / ----------- + ----------------------- | | ||- - + -------|*3 / ----------- + ----------------------- | \/ 7796595 *cos|---------------------------| \/ 2598865 *sin|---------------------------|| \/ 2598865 *cos|---------------------------| \/ 7796595 *sin|---------------------------|
2429 \\ 2 2 / \/ 2048383 16129 / | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = ---- - ------------------------------------------------------------------------- + I*|- ------------------------------------------------------------------------- - -------------------------------------------- + --------------------------------------------| + -------------------------------------------- + --------------------------------------------
381 48387 \ 48387 381 381 / 381 381
$$x_{2} = \frac{\sqrt{7796595} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{2429}{381} - \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + i \left(- \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} - \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387}\right)$$
_______________________________________
/ _______________
/ 18402860800 120*I*\/ 3378689085585
3 / ----------- + -----------------------
2429 10395460 \/ 2048383 16129
x3 = ---- - -------------------------------------------------- - --------------------------------------------
381 _______________________________________ 3
/ _______________
/ 18402860800 120*I*\/ 3378689085585
48387*3 / ----------- + -----------------------
\/ 2048383 16129
$$x_{3} = \frac{2429}{381} - \frac{\sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}{3} - \frac{10395460}{48387 \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}$$
x3 = 2429/381 - (18402860800/2048383 + 120*sqrt(3378689085585)*i/16129)^(1/3)/3 - 10395460/(48387*(18402860800/2048383 + 120*sqrt(3378689085585)*i/16129)^(1/3))
Suma y producto de raíces
[src]
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
10395460*re|------------------------------------------------------------| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| / / _______________\\ / / _______________\\ 10395460*re|------------------------------------------------------------| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| / / _______________\\ / / _______________\\
| _______________________________________| | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 || | _______________________________________| | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 || _______________________________________
|/ ___\ / _______________ | | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| |atan|---------------------|| |atan|---------------------|| |/ ___\ / _______________ | | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| |atan|---------------------|| |atan|---------------------|| / _______________
|| 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| _________ | \ 460071520 /| _________ | \ 460071520 /| || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| _________ | \ 460071520 /| _________ | \ 460071520 /| / 18402860800 120*I*\/ 3378689085585
||- - - -------|*3 / ----------- + ----------------------- | | ||- - - -------|*3 / ----------- + ----------------------- | \/ 2598865 *sin|---------------------------| \/ 7796595 *cos|---------------------------|| \/ 7796595 *sin|---------------------------| \/ 2598865 *cos|---------------------------| ||- - + -------|*3 / ----------- + ----------------------- | | ||- - + -------|*3 / ----------- + ----------------------- | \/ 7796595 *cos|---------------------------| \/ 2598865 *sin|---------------------------|| \/ 2598865 *cos|---------------------------| \/ 7796595 *sin|---------------------------| 3 / ----------- + -----------------------
2429 \\ 2 2 / \/ 2048383 16129 / | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| \ 3 / \ 3 / 2429 \\ 2 2 / \/ 2048383 16129 / | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| \ 3 / \ 3 / 2429 10395460 \/ 2048383 16129
---- - ------------------------------------------------------------------------- + I*|- ------------------------------------------------------------------------- + -------------------------------------------- + --------------------------------------------| - -------------------------------------------- + -------------------------------------------- + ---- - ------------------------------------------------------------------------- + I*|- ------------------------------------------------------------------------- - -------------------------------------------- + --------------------------------------------| + -------------------------------------------- + -------------------------------------------- + ---- - -------------------------------------------------- - --------------------------------------------
381 48387 \ 48387 381 381 / 381 381 381 48387 \ 48387 381 381 / 381 381 381 _______________________________________ 3
/ _______________
/ 18402860800 120*I*\/ 3378689085585
48387*3 / ----------- + -----------------------
\/ 2048383 16129
$$\left(\left(- \frac{\sqrt{7796595} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} - \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{\sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{2429}{381} + i \left(- \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381}\right)\right) + \left(\frac{\sqrt{7796595} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{2429}{381} - \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + i \left(- \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} - \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387}\right)\right)\right) + \left(\frac{2429}{381} - \frac{\sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}{3} - \frac{10395460}{48387 \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
10395460*re|------------------------------------------------------------| 10395460*re|------------------------------------------------------------| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| / / _______________\\
| _______________________________________| | _______________________________________| _______________________________________ | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | |381*\/ 3378689085585 ||
|/ ___\ / _______________ | |/ ___\ / _______________ | / _______________ | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| |atan|---------------------||
|| 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | / 18402860800 120*I*\/ 3378689085585 | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| _________ | \ 460071520 /|
||- - + -------|*3 / ----------- + ----------------------- | ||- - - -------|*3 / ----------- + ----------------------- | 3 / ----------- + ----------------------- | ||- - + -------|*3 / ----------- + ----------------------- | \/ 7796595 *cos|---------------------------| \/ 2598865 *sin|---------------------------|| | ||- - - -------|*3 / ----------- + ----------------------- | \/ 2598865 *sin|---------------------------| \/ 7796595 *cos|---------------------------|| 2*\/ 2598865 *cos|---------------------------|
2429 10395460 \\ 2 2 / \/ 2048383 16129 / \\ 2 2 / \/ 2048383 16129 / \/ 2048383 16129 | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| \ 3 /
---- - -------------------------------------------------- - ------------------------------------------------------------------------- - ------------------------------------------------------------------------- - -------------------------------------------- + I*|- ------------------------------------------------------------------------- - -------------------------------------------- + --------------------------------------------| + I*|- ------------------------------------------------------------------------- + -------------------------------------------- + --------------------------------------------| + ----------------------------------------------
127 _______________________________________ 48387 48387 3 \ 48387 381 381 / \ 48387 381 381 / 381
/ _______________
/ 18402860800 120*I*\/ 3378689085585
48387*3 / ----------- + -----------------------
\/ 2048383 16129
$$- \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} - \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{2 \sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{2429}{127} - \frac{\sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}{3} + i \left(- \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} - \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387}\right) + i \left(- \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381}\right) - \frac{10395460}{48387 \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}$$
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 10395460*re|------------------------------------------------------------| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| / / _______________\\ / / _______________\\| | 10395460*re|------------------------------------------------------------| | 10395460*im|------------------------------------------------------------| / / _______________\\ / / _______________\\| / / _______________\\ / / _______________\\|
| | _______________________________________| | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | | _______________________________________| | | _______________________________________| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 ||| / _______________________________________\
| |/ ___\ / _______________ | | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| |atan|---------------------|| |atan|---------------------||| | |/ ___\ / _______________ | | |/ ___\ / _______________ | |atan|---------------------|| |atan|---------------------||| |atan|---------------------|| |atan|---------------------||| | / _______________ |
| || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| _________ | \ 460071520 /| _________ | \ 460071520 /|| | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | | || 1 I*\/ 3 | / 18402860800 120*I*\/ 3378689085585 | _________ | \ 460071520 /| _________ | \ 460071520 /|| _________ | \ 460071520 /| _________ | \ 460071520 /|| | / 18402860800 120*I*\/ 3378689085585 |
| ||- - - -------|*3 / ----------- + ----------------------- | | ||- - - -------|*3 / ----------- + ----------------------- | \/ 2598865 *sin|---------------------------| \/ 7796595 *cos|---------------------------|| \/ 7796595 *sin|---------------------------| \/ 2598865 *cos|---------------------------|| | ||- - + -------|*3 / ----------- + ----------------------- | | ||- - + -------|*3 / ----------- + ----------------------- | \/ 7796595 *cos|---------------------------| \/ 2598865 *sin|---------------------------|| \/ 2598865 *cos|---------------------------| \/ 7796595 *sin|---------------------------|| | 3 / ----------- + ----------------------- |
|2429 \\ 2 2 / \/ 2048383 16129 / | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| \ 3 / \ 3 /| |2429 \\ 2 2 / \/ 2048383 16129 / | \\ 2 2 / \/ 2048383 16129 / \ 3 / \ 3 /| \ 3 / \ 3 /| |2429 10395460 \/ 2048383 16129 |
|---- - ------------------------------------------------------------------------- + I*|- ------------------------------------------------------------------------- + -------------------------------------------- + --------------------------------------------| - -------------------------------------------- + --------------------------------------------|*|---- - ------------------------------------------------------------------------- + I*|- ------------------------------------------------------------------------- - -------------------------------------------- + --------------------------------------------| + -------------------------------------------- + --------------------------------------------|*|---- - -------------------------------------------------- - --------------------------------------------|
\381 48387 \ 48387 381 381 / 381 381 / \381 48387 \ 48387 381 381 / 381 381 / |381 _______________________________________ 3 |
| / _______________ |
| / 18402860800 120*I*\/ 3378689085585 |
| 48387*3 / ----------- + ----------------------- |
\ \/ 2048383 16129 /
$$\left(- \frac{\sqrt{7796595} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} - \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{\sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{2429}{381} + i \left(- \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381}\right)\right) \left(\frac{\sqrt{7796595} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{2429}{381} - \frac{10395460 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387} + i \left(- \frac{\sqrt{7796595} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} + \frac{\sqrt{2598865} \sin{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}}{381} - \frac{10395460 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)}}{48387}\right)\right) \left(\frac{2429}{381} - \frac{\sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}{3} - \frac{10395460}{48387 \sqrt[3]{\frac{18402860800}{2048383} + \frac{120 \sqrt{3378689085585} i}{16129}}}\right)$$
=
/ / / _______________\\ / / _______________\\\
| | |381*\/ 3378689085585 || | |381*\/ 3378689085585 |||
/ _______________________________________ / _______________________________________\\ | |2*atan|---------------------|| |atan|---------------------|||
2/3 | 3 / _______________ | 3 / _______________ || | | \ 460071520 /| _________ | \ 460071520 /||
-5 *\5197730 - \/ 2300357600 + 1905*I*\/ 3378689085585 *\2429 - 2*\/ 2300357600 + 1905*I*\/ 3378689085585 //*|-4495419 + 20790920*cos|-----------------------------| + 9716*\/ 2598865 *cos|---------------------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_____________________________________
3 / _______________
276531705*\/ 460071520 + 381*I*\/ 3378689085585
$$- \frac{5^{\frac{2}{3}} \left(5197730 - \left(2429 - 2 \sqrt[3]{2300357600 + 1905 \sqrt{3378689085585} i}\right) \sqrt[3]{2300357600 + 1905 \sqrt{3378689085585} i}\right) \left(-4495419 + 9716 \sqrt{2598865} \cos{\left(\frac{\operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)} + 20790920 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{381 \sqrt{3378689085585}}{460071520} \right)}}{3} \right)}\right)}{276531705 \sqrt[3]{460071520 + 381 \sqrt{3378689085585} i}}$$
-5^(2/3)*(5197730 - (2300357600 + 1905*i*sqrt(3378689085585))^(1/3)*(2429 - 2*(2300357600 + 1905*i*sqrt(3378689085585))^(1/3)))*(-4495419 + 20790920*cos(2*atan(381*sqrt(3378689085585)/460071520)/3) + 9716*sqrt(2598865)*cos(atan(381*sqrt(3378689085585)/460071520)/3))/(276531705*(460071520 + 381*i*sqrt(3378689085585))^(1/3))
Respuesta numérica
[src]
x1 = 19.1291707834082
x2 = 9.63399486606545 + 1.0842021724855e-19*i
x3 = -9.63718139750518
x3 = -9.63718139750518