Find all triples $ (x,y,z)$ of positive real numbers which satisfy $ 2x^3 = 2y(x^2 + 1) - (z^2 + 1)$; $ 2y^4 = 3z(y^2 + 1) - 2(x^2 + 1)$; $ 2z^5 = 4x(z^2 + 1) - 3(y^2 + 1)$.
Source: Indonesia TST 2009, Test 5 P3
Tags: algebra proposed, algebra
Find all triples $ (x,y,z)$ of positive real numbers which satisfy $ 2x^3 = 2y(x^2 + 1) - (z^2 + 1)$; $ 2y^4 = 3z(y^2 + 1) - 2(x^2 + 1)$; $ 2z^5 = 4x(z^2 + 1) - 3(y^2 + 1)$.