Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 4"
Tigerzhang (talk | contribs) (→Solution 4) |
|||
(2 intermediate revisions by 2 users not shown) | |||
Line 10: | Line 10: | ||
<cmath>(x+8)(x-4) = 0</cmath> | <cmath>(x+8)(x-4) = 0</cmath> | ||
− | Thus, <math>x = - | + | Thus, <math>x = -8</math> or <math>x = 4</math>. Our answer is <math>(-8) \cdot 4=\boxed{-32}</math> |
~Bradygho | ~Bradygho | ||
Line 28: | Line 28: | ||
~tigerzhang | ~tigerzhang | ||
+ | |||
+ | |||
+ | |||
+ | ==See also== | ||
+ | #[[2021 JMPSC Accuracy Problems|Other 2021 JMPSC Accuracy Problems]] | ||
+ | #[[2021 JMPSC Accuracy Answer Key|2021 JMPSC Accuracy Answer Key]] | ||
+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
+ | {{JMPSC Notice}} |
Latest revision as of 17:23, 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.