2000 Pan African MO Problems/Problem 4
Problem
Let , and be real numbers such that , solve the system: in real numbers and .
Solution
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 .
See Also
2000 Pan African MO (Problems) | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All Pan African MO Problems and Solutions |