4

Part of 2010 Switzerland - Final Round

Problems(1)

Cyclic inequality in x,y,z

Source: Swiss Math Olympiad 2010 - final round, problem 4

x

y

z \in\mathbb{R}^+

xyz = 1

. Prove that \frac {(x + y - 1)^2}{z} + \frac {(y + z - 1)^2}{x} + \frac {(z + x - 1)^2}{y}\geqslant x + y + z\mbox{.}

inequalitiesalgebrafunctiontriangle inequalitythree variable inequality