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Find 'a' for which max(x)-min(x)=8

Source: P1: Bosnia and Herzegovina TST 2002

September 30, 2014

algebra proposedalgebra

Problem Statement

Let

x,y,z

be real numbers that satisfy

x+y+z= 3 \ \ \text{ and } \ \ xy+yz+zx= a

where

a

is a real parameter. Find the value of

a

for which the difference between the maximum and minimum possible values of

x

equals

8