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.

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 1 student sent a solution. 0 point: 1 student.

Problems in Mathematics of KöMaL, April 2014