Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 4"
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− | #[[2021 JMPSC Accuracy Problems|Other 2021 JMPSC | + | #[[2021 JMPSC Accuracy Problems|Other 2021 JMPSC Accuracy Problems]] |
− | #[[2021 JMPSC Accuracy Answer Key|2021 JMPSC | + | #[[2021 JMPSC Accuracy Answer Key|2021 JMPSC Accuracy Answer Key]] |
#[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
{{JMPSC Notice}} | {{JMPSC Notice}} |
Latest revision as of 16:23, 11 July 2021
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.