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