English Issue, December 2002
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New advanced problems - competition A
(302-304.)

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

f(x+y)+f(x)^.f(y)=f(xy)+f(x)+f(y)?