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All solutions for (x,y,z)

Source: Czech-Polish-Slovak 2008

April 13, 2013
algebrasystem of equationsalgebra proposed

Problem Statement

Determine all triples (x,y,z)(x, y, z) of positive real numbers which satisfies the following system of equations 2x3=2y(x2+1)−(z2+1),2x^3=2y(x^2+1)-(z^2+1), 2y4=3z(y2+1)−2(x2+1), 2y^4=3z(y^2+1)-2(x^2+1), 2z5=4x(z2+1)−3(y2+1). 2z^5=4x(z^2+1)-3(y^2+1).
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