Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 4"
Tigerzhang (talk | contribs) (→Solution 4) |
Tigerzhang (talk | contribs) (→Solution) |
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<cmath>x^2+ 4x + 4 = 36</cmath> | <cmath>x^2+ 4x + 4 = 36</cmath> | ||
<cmath>x^2 + 4x - 32 = 0</cmath> | <cmath>x^2 + 4x - 32 = 0</cmath> | ||
− | <cmath>(x | + | <cmath>(x+8)(x-4) = 0</cmath> |
− | Thus, <math>x = | + | Thus, <math>x = -88</math> or <math>x = 4</math>. Our answer is <math>(-8) \cdot 4=\boxed{-32}</math> |
~Bradygho | ~Bradygho |
Revision as of 11:39, 11 July 2021
Contents
[hide]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
.