Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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English Issue, December 2002

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New advanced problems - competition A

A. 302. Given the unit square ABCD and the point P on the plane, prove that

\(\displaystyle 3AP+5CP+\sqrt5(BP+DP)\ge6\sqrt2. \)

A. 303. x, y are non-negative numbers, and x3+y4\(\displaystyle \le\)x2+y3. Prove that

x3+y3\(\displaystyle \le\)2.

A. 304. Find all functions R+\(\displaystyle \mapsto\)R+, such that