(x-4)(x^2+16x+32)=13(x+8) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
/ / / _______\\ / / _______\\\ / / _______\\ / / _______\\
| | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||
| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|
| \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = -4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + --------------------------- - ---------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2
|3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || |
|\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
x1=−4−293sin(3atan(3828347))−93re(−21−23i)31026+2728347i1+231cos(3atan(3828347))+i−93im(−21−23i)31026+2728347i1+231sin(3atan(3828347))+293cos(3atan(3828347))
/ / / _______\\ / / _______\\\ / / _______\\ / / _______\\
| | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||
| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|
| \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = -4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + --------------------------- + ---------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2
|3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || |
|\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| |
\ \ 2 2 // \ \ \ 2 2 // /
x2=−4+293sin(3atan(3828347))+231cos(3atan(3828347))−93re(−21+23i)31026+2728347i1+i−293cos(3atan(3828347))+231sin(3atan(3828347))−93im(−21+23i)31026+2728347i1
_______________________
3 / _______
93 \/ 1026 + 27*I*\/ 28347
x3 = -4 - -------------------------- - --------------------------
_______________________ 3
3 / _______
\/ 1026 + 27*I*\/ 28347
x3=−4−331026+2728347i−31026+2728347i93
x3 = -4 - (1026 + 27*sqrt(28347)*i)^(1/3)/3 - 93/(1026 + 27*sqrt(28347)*i)^(1/3)
Suma y producto de raíces
[src]
/ / / _______\\ / / _______\\\ / / _______\\ / / _______\\ / / / _______\\ / / _______\\\ / / _______\\ / / _______\\
| | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 || | | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||
| |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------|| | |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||
| ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /| | ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /| _______________________
| \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------| | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------| 3 / _______
/ 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 / 93 \/ 1026 + 27*I*\/ 28347
-4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + --------------------------- - --------------------------- + -4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + --------------------------- + --------------------------- + -4 - -------------------------- - --------------------------
| _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 | _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 _______________________ 3
|3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | 3 / _______
|\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | \/ 1026 + 27*I*\/ 28347
\ \ 2 2 // \ \ \ 2 2 // / \ \ 2 2 // \ \ \ 2 2 // /
−4+293sin(3atan(3828347))+231cos(3atan(3828347))−93re(−21+23i)31026+2728347i1+i−293cos(3atan(3828347))+231sin(3atan(3828347))−93im(−21+23i)31026+2728347i1+−4−293sin(3atan(3828347))−93re(−21−23i)31026+2728347i1+231cos(3atan(3828347))+i−93im(−21−23i)31026+2728347i1+231sin(3atan(3828347))+293cos(3atan(3828347))+(−4−331026+2728347i−31026+2728347i93)
/ / / _______\\ / / _______\\\ / / / _______\\ / / _______\\\
| | |\/ 28347 || | |\/ 28347 ||| | | |\/ 28347 || | |\/ 28347 |||
| |atan|---------|| |atan|---------||| | |atan|---------|| |atan|---------||| / / _______\\
_______________________ | ____ | \ 38 /| ____ | \ 38 /|| | ____ | \ 38 /| ____ | \ 38 /|| | |\/ 28347 ||
3 / _______ | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| |atan|---------||
93 / 1 \ / 1 \ \/ 1026 + 27*I*\/ 28347 | / 1 \ \ 3 / \ 3 /| | / 1 \ \ 3 / \ 3 /| ____ | \ 38 /|
-12 - -------------------------- - 93*re|------------------------------------------| - 93*re|------------------------------------------| - -------------------------- + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + \/ 31 *cos|---------------|
_______________________ | _______________________ / ___\| | _______________________ / ___\| 3 | | _______________________ / ___\| 2 2 | | | _______________________ / ___\| 2 2 | \ 3 /
3 / _______ |3 / _______ | 1 I*\/ 3 || |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | | |3 / _______ | 1 I*\/ 3 || |
\/ 1026 + 27*I*\/ 28347 |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| |
\ \ 2 2 // \ \ 2 2 // \ \ \ 2 2 // / \ \ \ 2 2 // /
−12−93re(−21−23i)31026+2728347i1−93re(−21+23i)31026+2728347i1+31cos3atan(3828347)−331026+2728347i+i−93im(−21−23i)31026+2728347i1+231sin(3atan(3828347))+293cos(3atan(3828347))+i−293cos(3atan(3828347))+231sin(3atan(3828347))−93im(−21+23i)31026+2728347i1−31026+2728347i93
/ / / / _______\\ / / _______\\\ / / _______\\ / / _______\\\ / / / / _______\\ / / _______\\\ / / _______\\ / / _______\\\
| | | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 ||| | | | |\/ 28347 || | |\/ 28347 ||| | |\/ 28347 || | |\/ 28347 |||
| | |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------||| | | |atan|---------|| |atan|---------||| |atan|---------|| |atan|---------|||
| | ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|| | | ____ | \ 38 /| ____ | \ 38 /|| ____ | \ 38 /| ____ | \ 38 /|| / _______________________\
| | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|| | | \/ 31 *sin|---------------| \/ 93 *cos|---------------|| \/ 31 *cos|---------------| \/ 93 *sin|---------------|| | 3 / _______ |
| / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | / 1 \ | / 1 \ \ 3 / \ 3 /| \ 3 / \ 3 /| | 93 \/ 1026 + 27*I*\/ 28347 |
|-4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- + ---------------------------| + --------------------------- - ---------------------------|*|-4 - 93*re|------------------------------------------| + I*|- 93*im|------------------------------------------| + --------------------------- - ---------------------------| + --------------------------- + ---------------------------|*|-4 - -------------------------- - --------------------------|
| | _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 | | | _______________________ / ___\| | | _______________________ / ___\| 2 2 | 2 2 | | _______________________ 3 |
| |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | | | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || | | | 3 / _______ |
| |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - - -------|| | | | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | |\/ 1026 + 27*I*\/ 28347 *|- - + -------|| | | \ \/ 1026 + 27*I*\/ 28347 /
\ \ \ 2 2 // \ \ \ 2 2 // / / \ \ \ 2 2 // \ \ \ 2 2 // / /
−4−293sin(3atan(3828347))−93re(−21−23i)31026+2728347i1+231cos(3atan(3828347))+i−93im(−21−23i)31026+2728347i1+231sin(3atan(3828347))+293cos(3atan(3828347))−4+293sin(3atan(3828347))+231cos(3atan(3828347))−93re(−21+23i)31026+2728347i1+i−293cos(3atan(3828347))+231sin(3atan(3828347))−93im(−21+23i)31026+2728347i1(−4−331026+2728347i−31026+2728347i93)
/ / / _______\\ / / _______\\\
| | |\/ 28347 || | |\/ 28347 |||
/ __________________ / __________________\\ | |2*atan|---------|| |atan|---------|||
| 3 / _______ | 3 / _______ || | | \ 38 /| ____ | \ 38 /||
\31 + \/ 38 + I*\/ 28347 *\4 + \/ 38 + I*\/ 28347 //*|15 - 62*cos|-----------------| + 8*\/ 31 *cos|---------------||
\ \ 3 / \ 3 //
-------------------------------------------------------------------------------------------------------------------------
__________________
3 / _______
\/ 38 + I*\/ 28347
338+28347i(31+(4+338+28347i)338+28347i)(−62cos(32atan(3828347))+15+831cos(3atan(3828347)))
(31 + (38 + i*sqrt(28347))^(1/3)*(4 + (38 + i*sqrt(28347))^(1/3)))*(15 - 62*cos(2*atan(sqrt(28347)/38)/3) + 8*sqrt(31)*cos(atan(sqrt(28347)/38)/3))/(38 + i*sqrt(28347))^(1/3)