3 equations for 3 variables -- simple right?

Algebra Level 2

Let x, y and z be positive real numbers.

Given 3 equations:

1) \( x^{2} + y + z = 6 \)

2) \( x + y^{2} + z = 8 \)

3) \( x + y + z^{2} = 12 \)

Compute \( x^{7} + y^{4} + z \)

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