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sum (x^2+2)/\sqrt{z^2+xy} >=6

Source: Mathcenter Contest / Oly - Thai Forum 2009 R2 p3 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 9, 2022
algebrainequalities

Problem Statement

Let x,y,z>0 Prove that x2+2z2+xy+y2+2x2+yz+z2+2y2+zx≥6\frac{x^2+2}{\sqrt{z^2+xy}}+\dfrac{y^2+2}{\sqrt{x ^2+yz}}+\dfrac{z^2+2}{\sqrt{y^2+zx}}\geq 6. (nooonuii)
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