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Found problems: 26

2004 Unirea, 2

Find the maximum value of the expression $ x+y+z, $ where $ x,y,z $ are real numbers satisfying $$ \left\{ \begin{matrix} x^2+yz\le 2 \\y^2+zx\le 2\\ z^2+xy\le 2 \end{matrix} \right. . $$