MathDB

3

Part of 2009 Switzerland - Final Round

Problems(1)

sum (a-b)(b+c) >=0

Source: Switzerland - 2009 Swiss MO Final Round p3

12/26/2022
Let a,b,c,da, b, c, d be positive real numbers. Prove the following inequality and determine all cases in which the equality holds : a−bb+c+b−cc+d+c−dd+a+d−aa+b≥0.\frac{a - b}{b + c}+\frac{b - c}{c + d}+\frac{c - d}{d + a}+\frac{d - a}{a + b} \ge 0.
algebrainequalities