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max x-y where Σx=2 and Σxy=1

Source: Turkey Junior National Olympiad 2021 P3

January 7, 2022
inequalitiesmaximum valueFind maximum

Problem Statement

Let x,y,zx, y, z be real numbers such that x+y+z=2,        xy+yz+zx=1x+y+z=2, \;\;\;\; xy+yz+zx=1 Find the maximum possible value of x−yx-y.
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