The teacher will be very surprised to see your correct solution 😉
4 2 x - 5*x - 12*x + 46 = 0
sum
_____________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________________________________________ / _____________________ / _____________________ / _____________________ / _____________________ / / _______ / / _______ / / _______ / / _______ / 20 / 10099 I*\/ 30902 24 577 / 20 24 / 10099 I*\/ 30902 577 / 20 / 10099 I*\/ 30902 24 577 / 20 24 / 10099 I*\/ 30902 577 I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ / _____________________ / / _____________________ / _______ / _____________________ / / _____________________ / _______ / _____________________ / / _____________________ / _______ / _____________________ / / _____________________ / _______ / / _______ / / / _______ / 10099 I*\/ 30902 / / _______ / / / _______ / 10099 I*\/ 30902 / / _______ / / / _______ / 10099 I*\/ 30902 / / _______ / / / _______ / 10099 I*\/ 30902 / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / / _______ / / / _______ / / _______ / / / _______ / / _______ / / / _______ / / _______ / / / _______ / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- \/ \/ 216 4 \/ \/ \/ 216 4 \/ \/ 216 4 \/ \/ \/ 216 4 \/ \/ 216 4 \/ \/ \/ 216 4 \/ \/ 216 4 \/ \/ \/ 216 4 - ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + - ----------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2 2 2 2 2 2 2
=
0
product
/ _____________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________\ | / _____________________ | | / _____________________ | | / _____________________ | | / _____________________ | | / / _______ | | / / _______ | | / / _______ | | / / _______ | | / 20 / 10099 I*\/ 30902 24 577 | | / 20 24 / 10099 I*\/ 30902 577 | | / 20 / 10099 I*\/ 30902 24 577 | | / 20 24 / 10099 I*\/ 30902 577 | | I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- | | I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- | | I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- | | I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- | | ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ | | ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ | | ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ | | ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ | | / _____________________ / / _____________________ / _______ | | / _____________________ / / _____________________ / _______ | | / _____________________ / / _____________________ / _______ | | / _____________________ / / _____________________ / _______ | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / / _______ / / / _______ / 10099 I*\/ 30902 | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / _______ / / / _______ | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- | | \/ \/ 216 4 \/ \/ \/ 216 4 | |\/ \/ 216 4 \/ \/ \/ 216 4 | | \/ \/ 216 4 \/ \/ \/ 216 4 | |\/ \/ 216 4 \/ \/ \/ 216 4 | |- ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|----------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- ----------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
=
46
46
_____________________________________________________________________________________________________________________________________________________ / _____________________ / / _______ / 20 / 10099 I*\/ 30902 24 577 I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ / _____________________ / / _____________________ / _______ / / _______ / / / _______ / 10099 I*\/ 30902 / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / / _______ / / / _______ / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- \/ \/ 216 4 \/ \/ \/ 216 4 x1 = - ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2
_____________________________________________________________________________________________________________________________________________________ / _____________________ / / _______ / 20 24 / 10099 I*\/ 30902 577 I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ / _____________________ / / _____________________ / _______ / / _______ / / / _______ / 10099 I*\/ 30902 / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / / _______ / / / _______ / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- \/ \/ 216 4 \/ \/ \/ 216 4 x2 = ----------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2
_____________________________________________________________________________________________________________________________________________________ / _____________________ / / _______ / 20 / 10099 I*\/ 30902 24 577 I* / - -- + 2*3 / ----- + ----------- + ----------------------------------------------------------------------------- + ----------------------------- ___________________________________________________________________ / 3 \/ 216 4 ___________________________________________________________________ _____________________ / _____________________ / / _____________________ / _______ / / _______ / / / _______ / 10099 I*\/ 30902 / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / / _______ / / / _______ / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- \/ \/ 216 4 \/ \/ \/ 216 4 x3 = - ----------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2
_____________________________________________________________________________________________________________________________________________________ / _____________________ / / _______ / 20 24 / 10099 I*\/ 30902 577 I* / - -- - ----------------------------------------------------------------------------- + 2*3 / ----- + ----------- + ----------------------------- ___________________________________________________________________ / 3 ___________________________________________________________________ \/ 216 4 _____________________ / _____________________ / / _____________________ / _______ / / _______ / / / _______ / 10099 I*\/ 30902 / 10 / 10099 I*\/ 30902 577 / / 10 / 10099 I*\/ 30902 577 18*3 / ----- + ----------- / -- + 2*3 / ----- + ----------- + ----------------------------- / / -- + 2*3 / ----- + ----------- + ----------------------------- \/ 216 4 / 3 \/ 216 4 _____________________ / / 3 \/ 216 4 _____________________ / / _______ / / / _______ / / 10099 I*\/ 30902 / / / 10099 I*\/ 30902 / 18*3 / ----- + ----------- / / 18*3 / ----- + ----------- \/ \/ 216 4 \/ \/ \/ 216 4 x4 = ----------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- 2 2
x4 = sqrt(10/3 + 577/(18*(10099/216 + sqrt(30902)*i/4)^(1/3)) + 2*(10099/216 + sqrt(30902)*i/4)^(1/3))/2 + i*sqrt(-20/3 + 577/(18*(10099/216 + sqrt(30902)*i/4)^(1/3)) - 24/sqrt(10/3 + 577/(18*(10099/216 + sqrt(30902)*i/4)^(1/3)) + 2*(10099/216 + sqrt(30902)*i/4)^(1/3)) + 2*(10099/216 + sqrt(30902)*i/4)^(1/3))/2
x1 = 2.17045379174514 - 0.910313258851237*i
x2 = -2.17045379174514 + 1.89553926231068*i
x3 = -2.17045379174514 - 1.89553926231068*i
x4 = 2.17045379174514 + 0.910313258851237*i
x4 = 2.17045379174514 + 0.910313258851237*i