El profesor se sorprenderá mucho al ver tu solución correcta😉
3 2 x - 7*x - 20*x + 78 = 0
/ 1 \ / / 1 \ / / _______\\ / / _______\\\ / / _______\\ / / _______\\ 109*re|---------------------------------------| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | |9*\/ 15909 || | |9*\/ 15909 || | ____________________ / ___\| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| |atan|-----------|| |atan|-----------|| |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| _____ | \ 80 /| _____ | \ 80 /| |\/ 80 + 9*I*\/ 15909 *|- - - -------|| | |\/ 80 + 9*I*\/ 15909 *|- - - -------|| \/ 109 *sin|-----------------| \/ 327 *cos|-----------------|| \/ 327 *sin|-----------------| \/ 109 *cos|-----------------| 7 \ \ 2 2 // | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / x1 = - - ----------------------------------------------- + I*|- ----------------------------------------------- + ------------------------------ + ------------------------------| - ------------------------------ + ------------------------------ 3 3 \ 3 6 6 / 6 6
/ 1 \ / / 1 \ / / _______\\ / / _______\\\ / / _______\\ / / _______\\ 109*re|---------------------------------------| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | |9*\/ 15909 || | |9*\/ 15909 || | ____________________ / ___\| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| |atan|-----------|| |atan|-----------|| |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| _____ | \ 80 /| _____ | \ 80 /| |\/ 80 + 9*I*\/ 15909 *|- - + -------|| | |\/ 80 + 9*I*\/ 15909 *|- - + -------|| \/ 327 *cos|-----------------| \/ 109 *sin|-----------------|| \/ 109 *cos|-----------------| \/ 327 *sin|-----------------| 7 \ \ 2 2 // | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / x2 = - - ----------------------------------------------- + I*|- ----------------------------------------------- - ------------------------------ + ------------------------------| + ------------------------------ + ------------------------------ 3 3 \ 3 6 6 / 6 6
____________________ 3 / _______ 7 109 \/ 80 + 9*I*\/ 15909 x3 = - - ------------------------- - ----------------------- 3 ____________________ 3 3 / _______ 3*\/ 80 + 9*I*\/ 15909
x3 = 7/3 - (80 + 9*sqrt(15909)*i)^(1/3)/3 - 109/(3*(80 + 9*sqrt(15909)*i)^(1/3))
suma
/ 1 \ / / 1 \ / / _______\\ / / _______\\\ / / _______\\ / / _______\\ / 1 \ / / 1 \ / / _______\\ / / _______\\\ / / _______\\ / / _______\\ 109*re|---------------------------------------| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | |9*\/ 15909 || | |9*\/ 15909 || 109*re|---------------------------------------| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | |9*\/ 15909 || | |9*\/ 15909 || | ____________________ / ___\| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| |atan|-----------|| |atan|-----------|| | ____________________ / ___\| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| |atan|-----------|| |atan|-----------|| |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| _____ | \ 80 /| _____ | \ 80 /| |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| _____ | \ 80 /| _____ | \ 80 /| ____________________ |\/ 80 + 9*I*\/ 15909 *|- - - -------|| | |\/ 80 + 9*I*\/ 15909 *|- - - -------|| \/ 109 *sin|-----------------| \/ 327 *cos|-----------------|| \/ 327 *sin|-----------------| \/ 109 *cos|-----------------| |\/ 80 + 9*I*\/ 15909 *|- - + -------|| | |\/ 80 + 9*I*\/ 15909 *|- - + -------|| \/ 327 *cos|-----------------| \/ 109 *sin|-----------------|| \/ 109 *cos|-----------------| \/ 327 *sin|-----------------| 3 / _______ 7 \ \ 2 2 // | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / 7 \ \ 2 2 // | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 / 7 109 \/ 80 + 9*I*\/ 15909 - - ----------------------------------------------- + I*|- ----------------------------------------------- + ------------------------------ + ------------------------------| - ------------------------------ + ------------------------------ + - - ----------------------------------------------- + I*|- ----------------------------------------------- - ------------------------------ + ------------------------------| + ------------------------------ + ------------------------------ + - - ------------------------- - ----------------------- 3 3 \ 3 6 6 / 6 6 3 3 \ 3 6 6 / 6 6 3 ____________________ 3 3 / _______ 3*\/ 80 + 9*I*\/ 15909
=
/ 1 \ / 1 \ / / 1 \ / / _______\\ / / _______\\\ / / 1 \ / / _______\\ / / _______\\\ / / _______\\ 109*re|---------------------------------------| 109*re|---------------------------------------| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | |9*\/ 15909 || | ____________________ / ___\| | ____________________ / ___\| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| |atan|-----------|| |3 / _______ | 1 I*\/ 3 || |3 / _______ | 1 I*\/ 3 || ____________________ | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| _____ | \ 80 /| |\/ 80 + 9*I*\/ 15909 *|- - + -------|| |\/ 80 + 9*I*\/ 15909 *|- - - -------|| 3 / _______ | |\/ 80 + 9*I*\/ 15909 *|- - + -------|| \/ 327 *cos|-----------------| \/ 109 *sin|-----------------|| | |\/ 80 + 9*I*\/ 15909 *|- - - -------|| \/ 109 *sin|-----------------| \/ 327 *cos|-----------------|| \/ 109 *cos|-----------------| 109 \ \ 2 2 // \ \ 2 2 // \/ 80 + 9*I*\/ 15909 | \ \ 2 2 // \ 3 / \ 3 /| | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / 7 - ------------------------- - ----------------------------------------------- - ----------------------------------------------- - ----------------------- + I*|- ----------------------------------------------- - ------------------------------ + ------------------------------| + I*|- ----------------------------------------------- + ------------------------------ + ------------------------------| + ------------------------------ ____________________ 3 3 3 \ 3 6 6 / \ 3 6 6 / 3 3 / _______ 3*\/ 80 + 9*I*\/ 15909
producto
/ / 1 \ / / 1 \ / / _______\\ / / _______\\\ / / _______\\ / / _______\\\ / / 1 \ / / 1 \ / / _______\\ / / _______\\\ / / _______\\ / / _______\\\ | 109*re|---------------------------------------| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | |9*\/ 15909 || | |9*\/ 15909 ||| | 109*re|---------------------------------------| | 109*im|---------------------------------------| | |9*\/ 15909 || | |9*\/ 15909 ||| | |9*\/ 15909 || | |9*\/ 15909 ||| | | ____________________ / ___\| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| |atan|-----------|| |atan|-----------||| | | ____________________ / ___\| | | ____________________ / ___\| |atan|-----------|| |atan|-----------||| |atan|-----------|| |atan|-----------||| | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| _____ | \ 80 /| _____ | \ 80 /|| | |3 / _______ | 1 I*\/ 3 || | |3 / _______ | 1 I*\/ 3 || _____ | \ 80 /| _____ | \ 80 /|| _____ | \ 80 /| _____ | \ 80 /|| / ____________________\ | |\/ 80 + 9*I*\/ 15909 *|- - - -------|| | |\/ 80 + 9*I*\/ 15909 *|- - - -------|| \/ 109 *sin|-----------------| \/ 327 *cos|-----------------|| \/ 327 *sin|-----------------| \/ 109 *cos|-----------------|| | |\/ 80 + 9*I*\/ 15909 *|- - + -------|| | |\/ 80 + 9*I*\/ 15909 *|- - + -------|| \/ 327 *cos|-----------------| \/ 109 *sin|-----------------|| \/ 109 *cos|-----------------| \/ 327 *sin|-----------------|| | 3 / _______ | |7 \ \ 2 2 // | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| |7 \ \ 2 2 // | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / \ 3 /| |7 109 \/ 80 + 9*I*\/ 15909 | |- - ----------------------------------------------- + I*|- ----------------------------------------------- + ------------------------------ + ------------------------------| - ------------------------------ + ------------------------------|*|- - ----------------------------------------------- + I*|- ----------------------------------------------- - ------------------------------ + ------------------------------| + ------------------------------ + ------------------------------|*|- - ------------------------- - -----------------------| \3 3 \ 3 6 6 / 6 6 / \3 3 \ 3 6 6 / 6 6 / |3 ____________________ 3 | | 3 / _______ | \ 3*\/ 80 + 9*I*\/ 15909 /
=
/ / / _______\\ / / _______\\\ | | |9*\/ 15909 || | |9*\/ 15909 ||| / ____________________ / ____________________\\ | |2*atan|-----------|| |atan|-----------||| | 3 / _______ | 3 / _______ || | | \ 80 /| _____ | \ 80 /|| -\109 - \/ 80 + 9*I*\/ 15909 *\7 - \/ 80 + 9*I*\/ 15909 //*|-60 + 218*cos|-------------------| + 14*\/ 109 *cos|-----------------|| \ \ 3 / \ 3 // ---------------------------------------------------------------------------------------------------------------------------------------- ____________________ 3 / _______ 27*\/ 80 + 9*I*\/ 15909
-(109 - (80 + 9*i*sqrt(15909))^(1/3)*(7 - (80 + 9*i*sqrt(15909))^(1/3)))*(-60 + 218*cos(2*atan(9*sqrt(15909)/80)/3) + 14*sqrt(109)*cos(atan(9*sqrt(15909)/80)/3))/(27*(80 + 9*i*sqrt(15909))^(1/3))
x1 = -3.77433212570879
x2 = 8.27778023870892
x3 = 2.49655188699987
x3 = 2.49655188699987