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Regional Olympiad - FBH 2010 Grade 10 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018
algebrasystem of equations

Problem Statement

Find all real numbers (x,y)(x,y) satisfying the following: x+3x−yx2+y2=3x+\frac{3x-y}{x^2+y^2}=3 y−x+3yx2+y2=0y-\frac{x+3y}{x^2+y^2}=0
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