2002 Indonesia MO Problems/Problem 3
Find all real solutions from the following system of equations:
Square the first equation to get Subtract the second equation from the result to get Multiply the second equation by the first equation to get Subtract the third equation to get Cube the first equation to get If , , and , the solution triplet is the roots of the polynomial Factor the polynomial to get Since is a triple root to the polynomial, the only solution to the system of equations is , and plugging the values back in satisfies the system.
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