9.4

Part of 2011 All-Russian Olympiad Regional Round

Problems(1)

Inequality in three fractions

Source: Problem 4 of Russian Regional Olympiad 2011, grade 9

x

y

z

are positive real numbers. Prove the inequality

\frac{x+1}{y+1}+\frac{y+1}{z+1}+\frac{z+1}{x+1}\leq\frac{x}{y}+\frac{y}{z}+\frac{z}{x}.

(Authors: A. Khrabrov, B. Trushin)

inequalitiescalculusthree variable inequality