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 10 December 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. 
