2021 JMPSC Invitationals Problems/Problem 1
Revision as of 21:04, 11 July 2021 by Geometry285 (talk | contribs)
Contents
Problem
The equation where
is some constant, has
as a solution. What is the other solution?
Solution
Since must be a solution,
must be true. Therefore,
. We plug this back in to the original quadratic to get
. We can solve this quadratic to get
. We are asked to find the 2nd solution so our answer is
~Grisham
Solution 2
Plug to get
, so
, or
, meaning the other solution is
~Geometry285
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.