MathDB

2

Part of 2003 Kazakhstan National Olympiad

Problems(1)

sum x ^ 3/ (x + y) >= (xy + yz + zx)/2

Source: 2003 Kazakhstan MO grade XI P2

11/3/2020
For positive real numbers x,y,z x, y, z , prove the inequality: \displaylines {\frac {x ^ 3} {x + y} + \frac {y ^ 3} {y + z} + \frac {z ^ 3} {z + x} \geq \frac {xy + yz + zx} {2}.}
algebrainequalities