x*(x^2-1)-1*3/20=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
/ 1 \ / / 1 \ \
/ / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
| \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|
sin|--------------| ||- - - -------|*3 / -- + ---------- | | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|
\ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /
x1 = ------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------
2 3 \ 2 3 6 / 6
x1=−63cos(3atan(274071))+3re((−21−23i)3403+3604071i1)+2sin(3atan(274071))+i−2cos(3atan(274071))−63sin(3atan(274071))+3im((−21−23i)3403+3604071i1)
/ 1 \ / / 1 \ \
/ / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
| \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|
sin|--------------| ||- - + -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|
\ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /
x2 = - ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - -------------------------
2 3 \ 2 3 6 / 6
x2=3re((−21+23i)3403+3604071i1)−63cos(3atan(274071))−2sin(3atan(274071))+i3im((−21+23i)3403+3604071i1)−63sin(3atan(274071))+2cos(3atan(274071))
_________________
/ ______
/ 3 I*\/ 4071 1
x3 = 3 / -- + ---------- + ------------------------
\/ 40 360 _________________
/ ______
/ 3 I*\/ 4071
3*3 / -- + ----------
\/ 40 360
x3=33403+3604071i1+3403+3604071i
x3 = 1/(3*(3/40 + sqrt(4071)*i/360)^(1/3)) + (3/40 + sqrt(4071)*i/360)^(1/3)
Suma y producto de raíces
[src]
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
/ / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\ / / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 || | |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------|| |atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
| \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /| | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /| _________________
sin|--------------| ||- - - -------|*3 / -- + ---------- | | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------| sin|--------------| ||- - + -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------| / ______
\ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 / \ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 / / 3 I*\/ 4071 1
------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - ------------------------- + - ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - ------------------------- + 3 / -- + ---------- + ------------------------
2 3 \ 2 3 6 / 6 2 3 \ 2 3 6 / 6 \/ 40 360 _________________
/ ______
/ 3 I*\/ 4071
3*3 / -- + ----------
\/ 40 360
33403+3604071i1+3403+3604071i+3re((−21+23i)3403+3604071i1)−63cos(3atan(274071))−2sin(3atan(274071))+i3im((−21+23i)3403+3604071i1)−63sin(3atan(274071))+2cos(3atan(274071))+−63cos(3atan(274071))+3re((−21−23i)3403+3604071i1)+2sin(3atan(274071))+i−2cos(3atan(274071))−63sin(3atan(274071))+3im((−21−23i)3403+3604071i1)
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
re|--------------------------------------| re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\
| _________________| | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||
|/ ___\ / ______ | |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||
_________________ || 1 I*\/ 3 | / 3 I*\/ 4071 | || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|
/ ______ ||- - + -------|*3 / -- + ---------- | ||- - - -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|
/ 3 I*\/ 4071 1 \\ 2 2 / \/ 40 360 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /
3 / -- + ---------- + ------------------------ + ------------------------------------------ + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------
\/ 40 360 _________________ 3 3 \ 2 3 6 / \ 2 3 6 / 3
/ ______
/ 3 I*\/ 4071
3*3 / -- + ----------
\/ 40 360
−33cos(3atan(274071))+3re((−21+23i)3403+3604071i1)+3re((−21−23i)3403+3604071i1)+33403+3604071i1+i−2cos(3atan(274071))−63sin(3atan(274071))+3im((−21−23i)3403+3604071i1)+i3im((−21+23i)3403+3604071i1)−63sin(3atan(274071))+2cos(3atan(274071))+3403+3604071i
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| / / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\| | / / ______\\ re|--------------------------------------| | / / ______\\ im|--------------------------------------| / / ______\\| / / ______\\|
| | |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 ||| | | |\/ 4071 || | _________________| | | |\/ 4071 || | _________________| | |\/ 4071 ||| | |\/ 4071 |||
| |atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------||| | |atan|--------|| |/ ___\ / ______ | | |atan|--------|| |/ ___\ / ______ | |atan|--------||| |atan|--------|||
| | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|| | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | | | \ 27 /| || 1 I*\/ 3 | / 3 I*\/ 4071 | ___ | \ 27 /|| ___ | \ 27 /|| / _________________ \
|sin|--------------| ||- - - -------|*3 / -- + ---------- | | cos|--------------| ||- - - -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|| | sin|--------------| ||- - + -------|*3 / -- + ---------- | |cos|--------------| ||- - + -------|*3 / -- + ---------- | \/ 3 *sin|--------------|| \/ 3 *cos|--------------|| | / ______ |
| \ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /| | \ 3 / \\ 2 2 / \/ 40 360 / | \ 3 / \\ 2 2 / \/ 40 360 / \ 3 /| \ 3 /| | / 3 I*\/ 4071 1 |
|------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------|*|- ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - -------------------------|*|3 / -- + ---------- + ------------------------|
\ 2 3 \ 2 3 6 / 6 / \ 2 3 \ 2 3 6 / 6 / |\/ 40 360 _________________|
| / ______ |
| / 3 I*\/ 4071 |
| 3*3 / -- + ---------- |
\ \/ 40 360 /
−63cos(3atan(274071))+3re((−21−23i)3403+3604071i1)+2sin(3atan(274071))+i−2cos(3atan(274071))−63sin(3atan(274071))+3im((−21−23i)3403+3604071i1)3re((−21+23i)3403+3604071i1)−63cos(3atan(274071))−2sin(3atan(274071))+i3im((−21+23i)3403+3604071i1)−63sin(3atan(274071))+2cos(3atan(274071))33403+3604071i1+3403+3604071i
/ / / ______\\\
| | |\/ 4071 |||
| |2*atan|--------||| / 2/3\
| | \ 27 /|| | 3 ____ 3 ____ / ______\ |
|-12 + 24*cos|----------------||*\20*\/ 45 + \/ 75 *\27 + I*\/ 4071 / /
\ \ 3 //
--------------------------------------------------------------------------
_________________
3 / ______
1080*\/ 27 + I*\/ 4071
1080327+4071i(−12+24cos(32atan(274071)))(20345+375(27+4071i)32)
(-12 + 24*cos(2*atan(sqrt(4071)/27)/3))*(20*45^(1/3) + 75^(1/3)*(27 + i*sqrt(4071))^(2/3))/(1080*(27 + i*sqrt(4071))^(1/3))