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Superflous Symbols

Algebra Level 3

$\begin{array}{c} x(x+y+z)=26 \\ y(x+y+z)=27 \\z(x+y+z)=28 \end{array}$

How many triplets of real numbers $(x,y,z)$ satisfy the system of equations above?

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by Paola Ramírez

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