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x^4+y^2+4=5yz , y^4+z^2+4=5zx, z^4+x^2+4=5xy (3x3 system)

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2012 p6

February 13, 2020
system of equationsalgebra

Problem Statement

In the set of real numbers solve the system of equations x4+y2+4=5yzx^4+y^2+4=5yz y4+z2+4=5zxy^4+z^2+4=5zx z4+x2+4=5xyz^4+x^2+4=5xy
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