The teacher will be very surprised to see your correct solution 😉
x = 5^1/3
3 ___ x1 = \/ 5
3 ___ ___ 3 ___ \/ 5 I*\/ 3 *\/ 5 x2 = - ----- - ------------- 2 2
3 ___ ___ 3 ___ \/ 5 I*\/ 3 *\/ 5 x3 = - ----- + ------------- 2 2
x3 = -5^(1/3)/2 + sqrt(3)*5^(1/3)*i/2
sum
3 ___ ___ 3 ___ 3 ___ ___ 3 ___ 3 ___ \/ 5 I*\/ 3 *\/ 5 \/ 5 I*\/ 3 *\/ 5 \/ 5 + - ----- - ------------- + - ----- + ------------- 2 2 2 2
=
0
product
/ 3 ___ ___ 3 ___\ / 3 ___ ___ 3 ___\ 3 ___ | \/ 5 I*\/ 3 *\/ 5 | | \/ 5 I*\/ 3 *\/ 5 | \/ 5 *|- ----- - -------------|*|- ----- + -------------| \ 2 2 / \ 2 2 /
=
5
5
x1 = -0.854987973338349 - 1.48088260968236*i
x2 = -0.854987973338349 + 1.48088260968236*i
x3 = 1.7099759466767
x3 = 1.7099759466767