The teacher will be very surprised to see your correct solution 😉
4 3 2 6*x - x + 5*x - 1 = 0
__________________________________________________________________________________________________________________________________________________________ / ____________________ / / ________ / 79 / 2383 \/ 677109 47 119 / - -- - 2*3 / ----- + ---------- + ----------------------------- + ----------------------------------------------------------------------------------- / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ _____________________________________________________________________ / / ________ / ____________________ / ____________________ / / 2383 \/ 677109 / / ________ / / ________ / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / 79 / 2383 \/ 677109 47 / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / - --- + 2*3 / ----- + ---------- - ----------------------------- / / 144 \/ 93312 31104 ____________________ / 144 \/ 93312 31104 ____________________ / / / ________ / / ________ / / / 2383 \/ 677109 / / 2383 \/ 677109 / / 648*3 / ----- + ---------- / 648*3 / ----- + ---------- 1 \/ \/ \/ 93312 31104 \/ \/ 93312 31104 x1 = -- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- 24 2 2
__________________________________________________________________________________________________________________________________________________________ / ____________________ / / ________ / 79 / 2383 \/ 677109 47 119 / - -- - 2*3 / ----- + ---------- + ----------------------------- + ----------------------------------------------------------------------------------- _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ / ____________________ / / ________ / ____________________ / / ________ / / 2383 \/ 677109 / / ________ / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ / / ________ / / / ________ / / 2383 \/ 677109 / / / 2383 \/ 677109 / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- 1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 x2 = -- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 24 2 2
________________________________________________________________________________________________________________________________________________________ / ____________________ / / ________ / 79 / 2383 \/ 677109 47 119 I* / -- + 2*3 / ----- + ---------- - ----------------------------- + ----------------------------------------------------------------------------------- _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ / ____________________ / / ________ / ____________________ / / ________ / / 2383 \/ 677109 / / ________ / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ / / ________ / / / ________ / / 2383 \/ 677109 / / / 2383 \/ 677109 / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- 1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 x3 = -- + ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 24 2 2
________________________________________________________________________________________________________________________________________________________ / ____________________ / / ________ / 79 / 2383 \/ 677109 47 119 I* / -- + 2*3 / ----- + ---------- - ----------------------------- + ----------------------------------------------------------------------------------- _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ / ____________________ / / ________ / ____________________ / / ________ / / 2383 \/ 677109 / / ________ / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ / / ________ / / / ________ / / 2383 \/ 677109 / / / 2383 \/ 677109 / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- 1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 x4 = -- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 24 2 2
x4 = sqrt(-79/144 - 47/(648*(2383/93312 + sqrt(677109)/31104)^(1/3)) + 2*(2383/93312 + sqrt(677109)/31104)^(1/3))/2 + 1/24 + i*sqrt(-47/(648*(2383/93312 + sqrt(677109)/31104)^(1/3)) + 2*(2383/93312 + sqrt(677109)/31104)^(1/3) + 79/72 + 119/(864*sqrt(-79/144 - 47/(648*(2383/93312 + sqrt(677109)/31104)^(1/3)) + 2*(2383/93312 + sqrt(677109)/31104)^(1/3))))/2
sum
__________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________________________________ / ____________________ / ____________________ / ____________________ / ____________________ / / ________ / / ________ / / ________ / / ________ / 79 / 2383 \/ 677109 47 119 / 79 / 2383 \/ 677109 47 119 / 79 / 2383 \/ 677109 47 119 / 79 / 2383 \/ 677109 47 119 / - -- - 2*3 / ----- + ---------- + ----------------------------- + ----------------------------------------------------------------------------------- / - -- - 2*3 / ----- + ---------- + ----------------------------- + ----------------------------------------------------------------------------------- I* / -- + 2*3 / ----- + ---------- - ----------------------------- + ----------------------------------------------------------------------------------- I* / -- + 2*3 / ----- + ---------- - ----------------------------- + ----------------------------------------------------------------------------------- / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ / / ________ / ____________________ / ____________________ / ____________________ / / ________ / ____________________ / ____________________ / / ________ / ____________________ / ____________________ / / ________ / ____________________ / / 2383 \/ 677109 / / ________ / / ________ / / ________ / / 2383 \/ 677109 / / ________ / / ________ / / 2383 \/ 677109 / / ________ / / ________ / / 2383 \/ 677109 / / ________ / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / 79 / 2383 \/ 677109 47 / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / - --- + 2*3 / ----- + ---------- - ----------------------------- / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / / 144 \/ 93312 31104 ____________________ / 144 \/ 93312 31104 ____________________ / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ / / / ________ / / ________ / / ________ / / / ________ / / ________ / / / ________ / / ________ / / / ________ / / / 2383 \/ 677109 / / 2383 \/ 677109 / / 2383 \/ 677109 / / / 2383 \/ 677109 / / 2383 \/ 677109 / / / 2383 \/ 677109 / / 2383 \/ 677109 / / / 2383 \/ 677109 / / 648*3 / ----- + ---------- / 648*3 / ----- + ---------- / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- 1 \/ \/ \/ 93312 31104 \/ \/ 93312 31104 1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 -- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- + -- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -- + ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 24 2 2 24 2 2 24 2 2 24 2 2
=
1/6
product
/ __________________________________________________________________________________________________________________________________________________________ \ / __________________________________________________________________________________________________________________________________________________________\ / ________________________________________________________________________________________________________________________________________________________\ / ________________________________________________________________________________________________________________________________________________________\ | / ____________________ | | / ____________________ | | / ____________________ | | / ____________________ | | / / ________ | | / / ________ | | / / ________ | | / / ________ | | / 79 / 2383 \/ 677109 47 119 | | / 79 / 2383 \/ 677109 47 119 | | / 79 / 2383 \/ 677109 47 119 | | / 79 / 2383 \/ 677109 47 119 | | / - -- - 2*3 / ----- + ---------- + ----------------------------- + ----------------------------------------------------------------------------------- | | / - -- - 2*3 / ----- + ---------- + ----------------------------- + ----------------------------------------------------------------------------------- | | I* / -- + 2*3 / ----- + ---------- - ----------------------------- + ----------------------------------------------------------------------------------- | | I* / -- + 2*3 / ----- + ---------- - ----------------------------- + ----------------------------------------------------------------------------------- | | / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ _____________________________________________________________________| | _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ | | _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ | | _____________________________________________________________________ / 72 \/ 93312 31104 ____________________ _____________________________________________________________________ | | / / ________ / ____________________ / ____________________ | | / ____________________ / / ________ / ____________________ | | / ____________________ / / ________ / ____________________ | | / ____________________ / / ________ / ____________________ | | / / 2383 \/ 677109 / / ________ / / ________ | | / / ________ / / 2383 \/ 677109 / / ________ | | / / ________ / / 2383 \/ 677109 / / ________ | | / / ________ / / 2383 \/ 677109 / / ________ | | / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 / 79 / 2383 \/ 677109 47 | | / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 | | / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 | | / 79 / 2383 \/ 677109 47 / 648*3 / ----- + ---------- / 79 / 2383 \/ 677109 47 | | / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- / - --- + 2*3 / ----- + ---------- - ----------------------------- | | / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- | | / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- | | / - --- + 2*3 / ----- + ---------- - ----------------------------- / \/ 93312 31104 864* / - --- + 2*3 / ----- + ---------- - ----------------------------- | | / / 144 \/ 93312 31104 ____________________ / 144 \/ 93312 31104 ____________________ | | / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ | | / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ | | / 144 \/ 93312 31104 ____________________ / / 144 \/ 93312 31104 ____________________ | | / / / ________ / / ________ | | / / ________ / / / ________ | | / / ________ / / / ________ | | / / ________ / / / ________ | | / / / 2383 \/ 677109 / / 2383 \/ 677109 | | / / 2383 \/ 677109 / / / 2383 \/ 677109 | | / / 2383 \/ 677109 / / / 2383 \/ 677109 | | / / 2383 \/ 677109 / / / 2383 \/ 677109 | | / / 648*3 / ----- + ---------- / 648*3 / ----- + ---------- | | / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- | | / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- | | / 648*3 / ----- + ---------- / / 648*3 / ----- + ---------- | |1 \/ \/ \/ 93312 31104 \/ \/ 93312 31104 | |1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 | |1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 | |1 \/ \/ 93312 31104 \/ \/ \/ 93312 31104 | |-- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------|*|-- - ------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- + ------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- + ------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \24 2 2 / \24 2 2 / \24 2 2 / \24 2 2 /
=
-1/6
-1/6
x1 = 0.42098669378684
x2 = 0.0713686352156971 + 0.995981964434728*i
x3 = 0.0713686352156971 - 0.995981964434728*i
x4 = -0.397057297551568
x4 = -0.397057297551568