Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem B. 4703. (March 2015)

B. 4703. Given that the absolute values of the numbers \(\displaystyle x_1\), \(\displaystyle x_2\), \(\displaystyle x_3\), \(\displaystyle x_4\), \(\displaystyle x_5\), \(\displaystyle x_6\) are at most 1, and their sum is 0, prove that

\(\displaystyle 3\sum_{i=1}^{5} {\sqrt{1-x_i^2}} \le \sum_{i=1}^{5} {\sqrt{9-{(x_i+x_{i+1})}^2}}\,. \)

Suggested by K. Williams, Szeged

(6 pont)

Deadline expired on April 10, 2015.


2 students sent a solution.
4 points:1 student.
0 point:1 student.

Problems in Mathematics of KöMaL, March 2015