6

Part of 2007 Indonesia MO

Problems(1)

Simultaneous equations of three real numbers

Source: Indonesia Mathematics Olympiad 2007 Day 2 Problem 6

Find all triples

(x,y,z)

of real numbers which satisfy the simultaneous equations
x \equal{} y^3 \plus{} y \minus{} 8
y \equal{} z^3 \plus{} z \minus{} 8
z \equal{} x^3 \plus{} x \minus{} 8.

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