2021 JMPSC Accuracy Problems/Problem 4
Problem
If is its own reciprocal, find the product of all possible values of
Solution
From the problem, we know that
Thus, or
. Our answer is
~Bradygho
Solution 2
We have , so
. By Vieta's our roots
and
amount to
~Geometry285
Solution 3
Therefore, the product of the root is
~kante314
Solution 4
The only numbers that are their own reciprocals are and
. The equation
has the solution
, while the equation
has the solution
. The answer is
.
~tigerzhang