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.

### Statistics:

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

Problems in Mathematics of KöMaL, March 2015