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(6*x-5)*sqrt(2)*x^2-5*x+2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___ 2 (6*x - 5)*\/ 2 *x - 5*x + 2 = 0
$$\left(x^{2} \sqrt{2} \left(6 x - 5\right) - 5 x\right) + 2 = 0$$
Respuesta rápida
[src]
/ / / ___________________________________________\\ / / ___________________________________________\\\ / / ___________________________________________\\ / / ___________________________________________\\
| | | / 2 3 || | | / 2 3 ||| | | / 2 3 || | | / 2 3 ||
| | | / / ___\ / ___\ || | | / / ___\ / ___\ ||| | | / / ___\ / ___\ || | | / / ___\ / ___\ ||
| | | / | 125 11*\/ 2 | |25 5*\/ 2 | || | | / | 125 11*\/ 2 | |25 5*\/ 2 | ||| | | / | 125 11*\/ 2 | |25 5*\/ 2 | || | | / | 125 11*\/ 2 | |25 5*\/ 2 | ||
| | | / - |- --- + --------| + 4*|-- + -------| || | | / - |- --- + --------| + 4*|-- + -------| ||| | | / - |- --- + --------| + 4*|-- + -------| || | | / - |- --- + --------| + 4*|-- + -------| ||
| _____________________________________________________________ | |\/ \ 108 8 / \36 4 / || _____________________________________________________________ | |\/ \ 108 8 / \36 4 / ||| _____________________________________________________________ | |\/ \ 108 8 / \36 4 / || _____________________________________________________________ | |\/ \ 108 8 / \36 4 / ||
| / 2 |atan|-------------------------------------------------|| / 2 |atan|-------------------------------------------------||| / 2 |atan|-------------------------------------------------|| / 2 |atan|-------------------------------------------------||
| / / ___\ | | / ___\ || / / ___\ | | / ___\ ||| / / ___\ | | / ___\ || / / ___\ | | / ___\ ||
| / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | || / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | ||| / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | || / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | ||
| / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| || / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| ||| / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| || / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| ||
| / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /| ___ / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /|| / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /| ___ / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /|
|/ ___\ 6 / |- --- + --------| + |-- + -------| - ------------------- *sin|-------------------------------------------------------| \/ 3 *6 / |- --- + --------| + |-- + -------| - ------------------- *cos|-------------------------------------------------------|| / ___\ 6 / |- --- + --------| + |-- + -------| - ------------------- *cos|-------------------------------------------------------| \/ 3 *6 / |- --- + --------| + |-- + -------| - ------------------- *sin|-------------------------------------------------------|
5 || 25 5*\/ 2 | / 1 \ \/ \ 216 16 / \36 4 / 4 \ 3 / \/ \ 216 16 / \36 4 / 4 \ 3 /| | 25 5*\/ 2 | / 1 \ \/ \ 216 16 / \36 4 / 4 \ 3 / \/ \ 216 16 / \36 4 / 4 \ 3 /
x1 = -- + I*||- --- - -------|*im|---------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------| + |- --- - -------|*re|---------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------
18 |\ 108 12 / | ____________________________________________________________________| 6 6 | \ 108 12 / | ____________________________________________________________________| 6 6
| | / _________________________________________ | | | / _________________________________________ |
| | / / 2 3 | | | / / 2 3 |
| | / / / ___\ / ___\ | | | / / / ___\ / ___\ |
| | / / | 125 11*\/ 2 | |25 5*\/ 2 | | | | / / | 125 11*\/ 2 | |25 5*\/ 2 | |
| |/ ___\ / / |- --- + --------| - 4*|-- + -------| ___ | | |/ ___\ / / |- --- + --------| - 4*|-- + -------| ___ |
| || 1 I*\/ 3 | / 125 \/ \ 108 8 / \36 4 / 11*\/ 2 | | || 1 I*\/ 3 | / 125 \/ \ 108 8 / \36 4 / 11*\/ 2 |
| ||- - + -------|*3 / - --- + ----------------------------------------------- + -------- | | ||- - + -------|*3 / - --- + ----------------------------------------------- + -------- |
\ \\ 2 2 / \/ 216 2 16 / / \\ 2 2 / \/ 216 2 16 /
$$x_{1} = \frac{\sqrt{3} \sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6} + \frac{5}{18} + \left(- \frac{5 \sqrt{2}}{12} - \frac{25}{108}\right) \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{125}{216} + \frac{11 \sqrt{2}}{16} + \frac{\sqrt{- 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3} + \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}}{2}}}\right)} + i \left(- \frac{\sqrt{3} \sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6} + \left(- \frac{5 \sqrt{2}}{12} - \frac{25}{108}\right) \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{125}{216} + \frac{11 \sqrt{2}}{16} + \frac{\sqrt{- 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3} + \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}}{2}}}\right)}\right)$$
/ / / ___________________________________________\\ / / ___________________________________________\\\ / / ___________________________________________\\ / / ___________________________________________\\
| | | / 2 3 || | | / 2 3 ||| | | / 2 3 || | | / 2 3 ||
| | | / / ___\ / ___\ || | | / / ___\ / ___\ ||| | | / / ___\ / ___\ || | | / / ___\ / ___\ ||
| | | / | 125 11*\/ 2 | |25 5*\/ 2 | || | | / | 125 11*\/ 2 | |25 5*\/ 2 | ||| | | / | 125 11*\/ 2 | |25 5*\/ 2 | || | | / | 125 11*\/ 2 | |25 5*\/ 2 | ||
| | | / - |- --- + --------| + 4*|-- + -------| || | | / - |- --- + --------| + 4*|-- + -------| ||| | | / - |- --- + --------| + 4*|-- + -------| || | | / - |- --- + --------| + 4*|-- + -------| ||
| _____________________________________________________________ | |\/ \ 108 8 / \36 4 / || _____________________________________________________________ | |\/ \ 108 8 / \36 4 / ||| _____________________________________________________________ | |\/ \ 108 8 / \36 4 / || _____________________________________________________________ | |\/ \ 108 8 / \36 4 / ||
| / 2 |atan|-------------------------------------------------|| / 2 |atan|-------------------------------------------------||| / 2 |atan|-------------------------------------------------|| / 2 |atan|-------------------------------------------------||
| / / ___\ | | / ___\ || / / ___\ | | / ___\ ||| / / ___\ | | / ___\ || / / ___\ | | / ___\ ||
| / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | || / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | ||| / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | || / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | ||
| / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| || / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| ||| / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| || / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| ||
| / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /| ___ / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /|| / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /| ___ / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /|
|/ ___\ 6 / |- --- + --------| + |-- + -------| - ------------------- *sin|-------------------------------------------------------| \/ 3 *6 / |- --- + --------| + |-- + -------| - ------------------- *cos|-------------------------------------------------------|| / ___\ 6 / |- --- + --------| + |-- + -------| - ------------------- *cos|-------------------------------------------------------| \/ 3 *6 / |- --- + --------| + |-- + -------| - ------------------- *sin|-------------------------------------------------------|
5 || 25 5*\/ 2 | / 1 \ \/ \ 216 16 / \36 4 / 4 \ 3 / \/ \ 216 16 / \36 4 / 4 \ 3 /| | 25 5*\/ 2 | / 1 \ \/ \ 216 16 / \36 4 / 4 \ 3 / \/ \ 216 16 / \36 4 / 4 \ 3 /
x2 = -- + I*||- --- - -------|*im|---------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------| + |- --- - -------|*re|---------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------
18 |\ 108 12 / | ____________________________________________________________________| 6 6 | \ 108 12 / | ____________________________________________________________________| 6 6
| | / _________________________________________ | | | / _________________________________________ |
| | / / 2 3 | | | / / 2 3 |
| | / / / ___\ / ___\ | | | / / / ___\ / ___\ |
| | / / | 125 11*\/ 2 | |25 5*\/ 2 | | | | / / | 125 11*\/ 2 | |25 5*\/ 2 | |
| |/ ___\ / / |- --- + --------| - 4*|-- + -------| ___ | | |/ ___\ / / |- --- + --------| - 4*|-- + -------| ___ |
| || 1 I*\/ 3 | / 125 \/ \ 108 8 / \36 4 / 11*\/ 2 | | || 1 I*\/ 3 | / 125 \/ \ 108 8 / \36 4 / 11*\/ 2 |
| ||- - - -------|*3 / - --- + ----------------------------------------------- + -------- | | ||- - - -------|*3 / - --- + ----------------------------------------------- + -------- |
\ \\ 2 2 / \/ 216 2 16 / / \\ 2 2 / \/ 216 2 16 /
$$x_{2} = - \frac{\sqrt{3} \sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6} + \left(- \frac{5 \sqrt{2}}{12} - \frac{25}{108}\right) \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{125}{216} + \frac{11 \sqrt{2}}{16} + \frac{\sqrt{- 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3} + \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}}{2}}}\right)} + \frac{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6} + \frac{5}{18} + i \left(\left(- \frac{5 \sqrt{2}}{12} - \frac{25}{108}\right) \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{125}{216} + \frac{11 \sqrt{2}}{16} + \frac{\sqrt{- 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3} + \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}}{2}}}\right)} + \frac{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6} + \frac{\sqrt{3} \sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{6}\right)$$
/ / / ___________________________________________\\ / / ___________________________________________\\\ / / ___________________________________________\\ / / ___________________________________________\\
| | | / 2 3 || | | / 2 3 ||| | | / 2 3 || | | / 2 3 ||
| | | / / ___\ / ___\ || | | / / ___\ / ___\ ||| | | / / ___\ / ___\ || | | / / ___\ / ___\ ||
| | | / | 125 11*\/ 2 | |25 5*\/ 2 | || | | / | 125 11*\/ 2 | |25 5*\/ 2 | ||| | | / | 125 11*\/ 2 | |25 5*\/ 2 | || | | / | 125 11*\/ 2 | |25 5*\/ 2 | ||
| | | / - |- --- + --------| + 4*|-- + -------| || | | / - |- --- + --------| + 4*|-- + -------| ||| | | / - |- --- + --------| + 4*|-- + -------| || | | / - |- --- + --------| + 4*|-- + -------| ||
| _____________________________________________________________ | |\/ \ 108 8 / \36 4 / || | |\/ \ 108 8 / \36 4 / ||| _____________________________________________________________ | |\/ \ 108 8 / \36 4 / || | |\/ \ 108 8 / \36 4 / ||
| / 2 |atan|-------------------------------------------------|| |atan|-------------------------------------------------||| / 2 |atan|-------------------------------------------------|| |atan|-------------------------------------------------||
| / / ___\ | | / ___\ || | | / ___\ ||| / / ___\ | | / ___\ || | | / ___\ ||
| / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | || | | | 125 11*\/ 2 | ||| / 2 3 | 125 11*\/ 2 | | | | 125 11*\/ 2 | || | | | 125 11*\/ 2 | ||
| / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| || / ___\ | | 2*|- --- + --------| ||| / / ___\ / ___\ |- --- + --------| | | 2*|- --- + --------| || / ___\ | | 2*|- --- + --------| ||
| / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /| | 25 5*\/ 2 | | \ \ 216 16 / /|| / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | \ \ 216 16 / /| | 25 5*\/ 2 | | \ \ 216 16 / /|
| 6 / |- --- + --------| + |-- + -------| - ------------------- *sin|-------------------------------------------------------| |- --- - -------|*sin|-------------------------------------------------------|| 6 / |- --- + --------| + |-- + -------| - ------------------- *cos|-------------------------------------------------------| |- --- - -------|*cos|-------------------------------------------------------|
5 | \/ \ 216 16 / \36 4 / 4 \ 3 / \ 108 12 / \ 3 /| \/ \ 216 16 / \36 4 / 4 \ 3 / \ 108 12 / \ 3 /
x3 = -- + I*|- ---------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------
18 | 3 _____________________________________________________________ | 3 _____________________________________________________________
| / 2 | / 2
| / / ___\ | / / ___\
| / 2 3 | 125 11*\/ 2 | | / 2 3 | 125 11*\/ 2 |
| / / ___\ / ___\ |- --- + --------| | / / ___\ / ___\ |- --- + --------|
| / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 / | / | 125 11*\/ 2 | |25 5*\/ 2 | \ 108 8 /
| 6 / |- --- + --------| + |-- + -------| - ------------------- | 6 / |- --- + --------| + |-- + -------| - -------------------
\ \/ \ 216 16 / \36 4 / 4 / \/ \ 216 16 / \36 4 / 4
$$x_{3} = - \frac{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{3} + \frac{\left(- \frac{5 \sqrt{2}}{12} - \frac{25}{108}\right) \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}} + \frac{5}{18} + i \left(- \frac{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{3} - \frac{\left(- \frac{5 \sqrt{2}}{12} - \frac{25}{108}\right) \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{- \left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2} + 4 \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}{2 \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)} \right)}}{3} \right)}}{\sqrt[6]{- \frac{\left(- \frac{125}{108} + \frac{11 \sqrt{2}}{8}\right)^{2}}{4} + \left(- \frac{125}{216} + \frac{11 \sqrt{2}}{16}\right)^{2} + \left(\frac{25}{36} + \frac{5 \sqrt{2}}{4}\right)^{3}}}\right)$$
x3 = -(-(-125/108 + 11*sqrt(2)/8)^2/4 + (-125/216 + 11*sqrt(2)/16)^2 + (25/36 + 5*sqrt(2)/4)^3)^(1/6)*cos(atan(sqrt(-(-125/108 + 11*sqrt(2)/8)^2 + 4*(25/36 + 5*sqrt(2)/4)^3)/(2*(-125/216 + 11*sqrt(2)/16)))/3)/3 + (-5*sqrt(2)/12 - 25/108)*cos(atan(sqrt(-(-125/108 + 11*sqrt(2)/8)^2 + 4*(25/36 + 5*sqrt(2)/4)^3)/(2*(-125/216 + 11*sqrt(2)/16)))/3)/(-(-125/108 + 11*sqrt(2)/8)^2/4 + (-125/216 + 11*sqrt(2)/16)^2 + (25/36 + 5*sqrt(2)/4)^3)^(1/6) + 5/18 + i*(-(-(-125/108 + 11*sqrt(2)/8)^2/4 + (-125/216 + 11*sqrt(2)/16)^2 + (25/36 + 5*sqrt(2)/4)^3)^(1/6)*sin(atan(sqrt(-(-125/108 + 11*sqrt(2)/8)^2 + 4*(25/36 + 5*sqrt(2)/4)^3)/(2*(-125/216 + 11*sqrt(2)/16)))/3)/3 - (-5*sqrt(2)/12 - 25/108)*sin(atan(sqrt(-(-125/108 + 11*sqrt(2)/8)^2 + 4*(25/36 + 5*sqrt(2)/4)^3)/(2*(-125/216 + 11*sqrt(2)/16)))/3)/(-(-125/108 + 11*sqrt(2)/8)^2/4 + (-125/216 + 11*sqrt(2)/16)^2 + (25/36 + 5*sqrt(2)/4)^3)^(1/6))
Respuesta numérica
[src]
x1 = 0.313353382043293
x2 = 1.1654113774001
x3 = -0.645431426110057
x3 = -0.645431426110057