Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 4"
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− | The only numbers that are their own reciprocals are <math>1</math> and <math>-1</math>. The equation <math>\frac{x+2}{6}=1</math> has the solution <math>x=4</math>, while the equation <math>\frac{x+2}{6}=-1</math> has the solution <math>x=-8</math>. The answer is <math>4-8=\boxed{- | + | The only numbers that are their own reciprocals are <math>1</math> and <math>-1</math>. The equation <math>\frac{x+2}{6}=1</math> has the solution <math>x=4</math>, while the equation <math>\frac{x+2}{6}=-1</math> has the solution <math>x=-8</math>. The answer is <math>4 \cdot (-8)=\boxed{-32}</math>. |
Revision as of 12:38, 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 .