MathDB

A1

Part of 2022-IMOC

Problems(1)

Strict Inequality with cyclic sums

Source: 2022 IMOC A1

9/5/2022
If positive real numbers x,y,zx,y,z satisfies x+y+z=3,x+y+z=3, prove that ∑cycy2z2<3+∑cycyz.\sum_{\text{cyc}} y^2z^2<3+\sum_{\text{cyc}} yz.
Proposed by Li4 and Untro368.
inequalities