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Find min/max of x+y+z-xy-yz-zx

Source: Canadian Repêchage 2013: Problem 6

May 20, 2014
inequalities proposedinequalities

Problem Statement

Let x,y,zx, y, z be real numbers that are greater than or equal to 00 and less than or equal to 12\frac{1}{2}

[*] (a) Determine the minimum possible value of x+y+z−xy−yz−zxx+y+z-xy-yz-zx and determine all triples (x,y,z)(x,y,z) for which this minimum is obtained.
[*] (b) Determine the maximum possible value of x+y+z−xy−yz−zxx+y+z-xy-yz-zx and determine all triples (x,y,z)(x,y,z) for which this maximum is obtained.
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