2021 JMPSC Invitationals Problems/Problem 8
Problem
Let and be real numbers that satisfy Find .
Solution
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
Solution 2
Each number shares are factor of , which means , or and . We see and , so
~Geometry285
Solution 3
Multiplying the equations together, we get Therefore, Subtracting the equations, we get and , therefore,
- kante314 -
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.