Baltic Way 2022 · Problem 4

Algebra

The positive real numbers $x,y,z$ satisfy $xy+yz+zx=1$ . Prove that

2(x^2+y^2+z^2)+\frac43\left(\frac1{x^2+1}+\frac1{y^2+1}+\frac1{z^2+1}\right)\ge5.

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Review

Equations and inequalities

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Results from Baltic Way 2022

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