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sumx/\sqrt {x + y} >= \sqrt [4]{\frac {27(yz + zx + xy)}{4}}

Source: Mathcenter Contest / Oly - Thai Forum 2008 R2 p1 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 11, 2022
algebrainequalities

Problem Statement

Let x,y,zx,y,z be a positive real numbers. Prove that xx+y+yy+z+zz+x≥27(yz+zx+xy)44\frac {x}{\sqrt {x + y}} + \frac {y}{\sqrt {y + z}} + \frac { z}{\sqrt {z + x}}\geq\sqrt [4]{\frac {27(yz + zx + xy)}{4}}
(dektep)
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