Difference between revisions of "2002 Indonesia MO Problems/Problem 3"
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==See Also== | ==See Also== | ||
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[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] |
Latest revision as of 00:09, 4 August 2018
Problem
Find all real solutions from the following system of equations:
Solution
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.
See Also
2002 Indonesia MO (Problems) | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 • 7 | Followed by Problem 4 |
All Indonesia MO Problems and Solutions |