4

Part of 2008 German National Olympiad

Problems(1)

Find smallest C such that 1+(x+y)² <= C·(1+x²)·(1+y²)

Source: German DEMO 2008, grade 11-13, round 4, problem 4

Find the smallest constant

C

such that for all real

x,y

1\plus{}(x\plus{}y)^2 \leq C \cdot (1\plus{}x^2) \cdot (1\plus{}y^2) holds.

functioninequalities