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Find the greatest value and the smallest value of x+y

Source: VietnamMO2005,problem1

March 10, 2005
inequalities proposedinequalitiesalgebraVietnam

Problem Statement

Let x,yx,y be real numbers satisfying the condition: x−3x+1=3y+2−yx-3\sqrt {x+1}=3\sqrt{y+2} -y Find the greatest value and the smallest value of: P=x+yP=x+y
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