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System of equatins

Source: Moldova Junior TST 2008 Day 3 Problem 1

April 11, 2008
inequalitiesalgebra proposedalgebra

Problem Statement

Find all triplets (x,y,z) (x,y,z), that satisfy: {  x2−2x−4z=3 y2−2y−2x=−14 z2−4y−4z=−18 \{\begin{array}{c}\ \ x^2 - 2x - 4z = 3\ y^2 - 2y - 2x = - 14 \ z^2 - 4y - 4z = - 18 \end{array}
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