El profesor se sorprenderá mucho al ver tu solución correcta😉
(x - 2)*(x - 4)*(x - 7) = x
suma
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \ 22*re|---------------------------------------| |22*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ 22*re|---------------------------------------| |22*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ | __________________| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | |3*\/ 1407 || | |3*\/ 1407 || | __________________| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | |3*\/ 1407 || | |3*\/ 1407 || |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| || 1 I*\/ 3 | / 173 I*\/ 1407 | | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| ____ | \ 173 /| ____ | \ 173 /| || 1 I*\/ 3 | / 173 I*\/ 1407 | | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| ____ | \ 173 /| ____ | \ 173 /| __________________ ||- - - -------|*3 / --- + ---------- | | ||- - - -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| \/ 22 *cos|----------------| \/ 66 *sin|----------------| ||- - + -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| \/ 22 *cos|----------------| \/ 66 *sin|----------------| / ______ 13 \\ 2 2 / \/ 54 18 / | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| \ 3 / \ 3 / 13 \\ 2 2 / \/ 54 18 / | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| \ 3 / \ 3 / 13 / 173 I*\/ 1407 22 -- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ---------------------------- + ---------------------------- + -- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| - ---------------------------- - ---------------------------- + -- + 3 / --- + ---------- + ------------------------- 3 9 \ 9 6 6 / 6 6 3 9 \ 9 6 6 / 6 6 3 \/ 54 18 __________________ / ______ / 173 I*\/ 1407 9*3 / --- + ---------- \/ 54 18
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \ 22*re|---------------------------------------| 22*re|---------------------------------------| |22*im|---------------------------------------| / / ______\\ / / ______\\| |22*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ | __________________| | __________________| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | |3*\/ 1407 || |/ ___\ / ______ | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| __________________ || 1 I*\/ 3 | / 173 I*\/ 1407 | || 1 I*\/ 3 | / 173 I*\/ 1407 | | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| ____ | \ 173 /| / ______ ||- - + -------|*3 / --- + ---------- | ||- - - -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| | ||- - - -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| \/ 22 *cos|----------------| / 173 I*\/ 1407 22 \\ 2 2 / \/ 54 18 / \\ 2 2 / \/ 54 18 / | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| \ 3 / 13 + 3 / --- + ---------- + ------------------------- + ---------------------------------------------- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ---------------------------- \/ 54 18 __________________ 9 9 \ 9 6 6 / \ 9 6 6 / 3 / ______ / 173 I*\/ 1407 9*3 / --- + ---------- \/ 54 18
producto
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \ | 22*re|---------------------------------------| |22*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| | 22*re|---------------------------------------| |22*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| | | __________________| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | |3*\/ 1407 || | |3*\/ 1407 ||| | | __________________| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | |3*\/ 1407 || | |3*\/ 1407 ||| | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | || 1 I*\/ 3 | / 173 I*\/ 1407 | | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| ____ | \ 173 /| ____ | \ 173 /|| | || 1 I*\/ 3 | / 173 I*\/ 1407 | | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| ____ | \ 173 /| ____ | \ 173 /|| / __________________ \ | ||- - - -------|*3 / --- + ---------- | | ||- - - -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| \/ 22 *cos|----------------| \/ 66 *sin|----------------|| | ||- - + -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| \/ 22 *cos|----------------| \/ 66 *sin|----------------|| | / ______ | |13 \\ 2 2 / \/ 54 18 / | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| \ 3 / \ 3 /| |13 \\ 2 2 / \/ 54 18 / | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| \ 3 / \ 3 /| |13 / 173 I*\/ 1407 22 | |-- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ---------------------------- + ----------------------------|*|-- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| - ---------------------------- - ----------------------------|*|-- + 3 / --- + ---------- + -------------------------| \3 9 \ 9 6 6 / 6 6 / \3 9 \ 9 6 6 / 6 6 / |3 \/ 54 18 __________________| | / ______ | | / 173 I*\/ 1407 | | 9*3 / --- + ---------- | \ \/ 54 18 /
=
/ / / ______\\ / / ______\\\ | | |3*\/ 1407 || | |3*\/ 1407 ||| / ____________________ / ____________________\\ | |2*atan|----------|| |atan|----------||| | 3 ___ 3 / ______ | 2/3 3 / ______ || | | \ 173 /| ____ | \ 173 /|| \44*\/ 2 + \/ 173 + 3*I*\/ 1407 *\26 + 2 *\/ 173 + 3*I*\/ 1407 //*|147 + 44*cos|------------------| - 26*\/ 22 *cos|----------------|| \ \ 3 / \ 3 // --------------------------------------------------------------------------------------------------------------------------------------------- ____________________ 3 / ______ 54*\/ 173 + 3*I*\/ 1407
(44*2^(1/3) + (173 + 3*i*sqrt(1407))^(1/3)*(26 + 2^(2/3)*(173 + 3*i*sqrt(1407))^(1/3)))*(147 + 44*cos(2*atan(3*sqrt(1407)/173)/3) - 26*sqrt(22)*cos(atan(3*sqrt(1407)/173)/3))/(54*(173 + 3*i*sqrt(1407))^(1/3))
/ 1 \ / / 1 \ \ 22*re|---------------------------------------| |22*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ | __________________| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | |3*\/ 1407 || | |3*\/ 1407 || |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| || 1 I*\/ 3 | / 173 I*\/ 1407 | | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| ____ | \ 173 /| ____ | \ 173 /| ||- - - -------|*3 / --- + ---------- | | ||- - - -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| \/ 22 *cos|----------------| \/ 66 *sin|----------------| 13 \\ 2 2 / \/ 54 18 / | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| \ 3 / \ 3 / x1 = -- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ---------------------------- + ---------------------------- 3 9 \ 9 6 6 / 6 6
/ 1 \ / / 1 \ \ 22*re|---------------------------------------| |22*im|---------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ | __________________| | | __________________| | |3*\/ 1407 || | |3*\/ 1407 ||| | |3*\/ 1407 || | |3*\/ 1407 || |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| || 1 I*\/ 3 | / 173 I*\/ 1407 | | || 1 I*\/ 3 | / 173 I*\/ 1407 | ____ | \ 173 /| ____ | \ 173 /|| ____ | \ 173 /| ____ | \ 173 /| ||- - + -------|*3 / --- + ---------- | | ||- - + -------|*3 / --- + ---------- | \/ 22 *sin|----------------| \/ 66 *cos|----------------|| \/ 22 *cos|----------------| \/ 66 *sin|----------------| 13 \\ 2 2 / \/ 54 18 / | \\ 2 2 / \/ 54 18 / \ 3 / \ 3 /| \ 3 / \ 3 / x2 = -- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| - ---------------------------- - ---------------------------- 3 9 \ 9 6 6 / 6 6
__________________ / ______ 13 / 173 I*\/ 1407 22 x3 = -- + 3 / --- + ---------- + ------------------------- 3 \/ 54 18 __________________ / ______ / 173 I*\/ 1407 9*3 / --- + ---------- \/ 54 18
x3 = 13/3 + 22/(9*(173/54 + sqrt(1407)*i/18)^(1/3)) + (173/54 + sqrt(1407)*i/18)^(1/3)
x1 = 7.40267882952119
x2 = 3.31603086087073
x3 = 2.28129030960809
x3 = 2.28129030960809