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x,y,z system of equations

Source: IberoAmerican 1989 Q1

November 27, 2010
algebrasystem of equationsalgebra proposed

Problem Statement

Determine all triples of real numbers that satisfy the following system of equations: x+y−z=−1x2−y2+z2=1−x3+y3+z3=−1x+y-z=-1\\ x^2-y^2+z^2=1\\ -x^3+y^3+z^3=-1
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