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x+y+z=xy+yz+zx and xyz=1 , x,y,z>0 with min sum

Source: Greece JBMO TST 2009 p4

April 29, 2019
algebrasystem of equationsminimumSum

Problem Statement

Find positive real numbers x,y,zx,y,z that are solutions of the system x+y+z=xy+yz+zxx+y+z=xy+yz+zx and xyz=1xyz=1 , and have the smallest possible sum.
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