2021 JMPSC Invitationals Problems/Problem 8
Contents
[hide]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
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