Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4667. (November 2014)

B. 4667. Prove that if $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$ are the sides of a triangle of unit perimeter, then $\displaystyle a^2+b^2+c^2+4abc<\frac{1}{2}$.

(5 pont)

Deadline expired on December 10, 2014.

### Statistics:

 90 students sent a solution. 5 points: 75 students. 4 points: 2 students. 3 points: 1 student. 2 points: 1 student. 1 point: 3 students. 0 point: 8 students.

Problems in Mathematics of KöMaL, November 2014