2000 Pan African MO Problems/Problem 4
Let , and be real numbers such that , solve the system: in real numbers and .
Expanding the last equation and simplifying results in Isolating means that . Substituting in the second equation results in By the Zero Product Property, . If , then either or . Thus, ordered pair can be or . Otherwise, , so another ordered pair can be . Setting means that the ordered pair can be rewritten as .
Because the case is part of , the ordered pairs that are solutions are .
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