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
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.