2018 AIME I Problems/Problem 5
For each ordered pair of real numbers satisfying
there is a real number
such that
Find the product of all possible values of
.
Solutions
Straightforward Solution
Note that . DO NOT SQUARE THE WRONG SIDE!
That gives
upon simplification and division by
. Then,
or
.
From the second equation,
. If we take
, we see that
. If we take
, we see that
. The product is
.