Geodesic
On solving cubic equations in square radicals
Matematičeskoe obrazovanie, no. 1 (2024), pp. 18-21 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Examples are given of parametric families of equations of the third and sixth degree, for which all roots are expressed through square radicals. A condition has been found under which a sixth-degree polynomial in canonical form can be represented as a product of third-degree polynomials in canonical form. 
@article{MO_2024_1_a2,
     author = {N. S. Astapov and N. K. Noland},
     title = {On solving cubic equations in square radicals},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {18--21},
     year = {2024},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2024_1_a2/}
}
TY  - JOUR
AU  - N. S. Astapov
AU  - N. K. Noland
TI  - On solving cubic equations in square radicals
JO  - Matematičeskoe obrazovanie
PY  - 2024
SP  - 18
EP  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MO_2024_1_a2/
LA  - ru
ID  - MO_2024_1_a2
ER  - 
%0 Journal Article
%A N. S. Astapov
%A N. K. Noland
%T On solving cubic equations in square radicals
%J Matematičeskoe obrazovanie
%D 2024
%P 18-21
%N 1
%U http://geodesic.mathdoc.fr/item/MO_2024_1_a2/
%G ru
%F MO_2024_1_a2
N. S. Astapov; N. K. Noland. On solving cubic equations in square radicals. Matematičeskoe obrazovanie, no. 1 (2024), pp. 18-21. http://geodesic.mathdoc.fr/item/MO_2024_1_a2/

[1] N. S. Astapov, I. S. Astapov, “Sravnitelnyi analiz reshenii algebraicheskikh uravnenii tretei i chetvertoi stepeni”, Sibirskii zhurnal chistoi i prikladnoi matematiki, 16:1 (2016), 14–28 | MR | Zbl

[2] S. I. Schmakov, “A Universal Method of Solving Quartic Equations”, International Journal of Pure and Applied Mathematics, 71:2 (2011), 251–259 | MR

[3] M. Hajja, J. Sondow, “Newton Quadrilaterals, the Associated Cubic Equations, and Their Rational Solutions”, Amer. Math. Monthly, 126 (2019), 135–150 | DOI | MR | Zbl

[4] N. S. Astapov, “O reshenii v kvadratnykh radikalakh algebraicheskikh uravnenii malykh stepenei”, Vestnik YuUrGU. Seriya “Matematika. Mekhanika. Fizika”, 14:3 (2022), 5–16 | Zbl

[5] L. I. Galieva, I. G. Galyautdinov, “Ob odnom klasse uravnenii, razreshimykh v radikalakh”, Izvestiya vuzov. Matematika, 2011, no. 2, 22–30 | MR | Zbl

[6] I. A. Antipova, E. N. Mikhalkin, A. K. Tsikh, “Ratsionalnye vyrazheniya dlya kratnykh kornei algebraicheskikh uravnenii”, Matem. sb., 209:10 (2018), 3–30 | Zbl

[7] Yu. V. Trubnikov, M. M. Chernyavskii, “Lokalizatsiya i nakhozhdenie reshenii trekhchlennykh algebraicheskikh uravnenii”, Matematicheskie struktury i modelirovanie, 2020, no. 2 (54), 65–85