2021 JMPSC Invitationals Problems/Problem 8
Let and be real numbers that satisfy Find .
We let and to get the new system of equations Multiplying these two, we have or We divide by to get and divide by to get . Recall that and . Solving the system of equations we get and . This means that ~samrocksnature
Each number shares are factor of , which means , or and . We see and , so
Multiplying the equations together, we get Therefore, Subtracting the equations, we get and , therefore,
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