Mathematical and Physical Journal
for High Schools
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Problem B. 4784. (March 2016)

B. 4784. Prove that the following inequality is true for all real numbers \(\displaystyle a\), \(\displaystyle b\), \(\displaystyle c\):

\(\displaystyle 2\big(a^4+b^4+c^4\big)+\frac{71+17\sqrt{17}}{2}\ge 4abc+ a^2b^2+c^2a^2+3b^2c^2. \)

Proposed by M. Sawhney, Commack, NY, USA

(6 pont)

Deadline expired on April 11, 2016.


Statistics:

22 students sent a solution.
6 points:Andó Angelika, Borbényi Márton, Fajszi Bulcsú, Glasznova Maja, Horváth András János, Imolay András, Klász Viktória, Kocsis Júlia, Lajkó Kálmán, Matolcsi Dávid, Németh 123 Balázs, Polgár Márton, Szemerédi Levente, Tiszay Ádám, Tóth Viktor, Vághy Mihály.
5 points:Keresztes László, Váli Benedek.
4 points:1 student.
2 points:1 student.
1 point:1 student.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, March 2016