sum x ^ 3/ (x + y) >= (xy + yz + zx)/2
Source: 2003 Kazakhstan MO grade XI P2
November 3, 2020
algebrainequalities
Problem Statement
For positive real numbers , 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}.}