MathDB

6

Part of 2013 Canadian Mathematical Olympiad Qualification Repechage

Problems(1)

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

Source: Canadian Repêchage 2013: Problem 6

5/20/2014
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.
inequalities proposedinequalities