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Strict Inequality with cyclic sums

Source: 2022 IMOC A1

September 5, 2022
inequalities

Problem Statement

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.
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