Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem A. 616. (April 2014)

A. 616. Prove that

\(\displaystyle \left(\frac{1+a}2\right)^{2x(x+y)} \left(\frac{1+b}2\right)^{2y(x+y)} \ge a^{x^2} b^{y^2} \left(\frac{a+b}2\right)^{2xy} \)

holds for all real numbers \(\displaystyle a,b>0\) and \(\displaystyle x\), \(\displaystyle y\).

(5 pont)

Deadline expired on May 12, 2014.

1 student sent a solution.

0 point: 1 student.