Difference between revisions of "2017 AMC 8 Problems/Problem 21"
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Revision as of 22:28, 26 December 2023
Contents
[hide]Problem
Suppose ,
, and
are nonzero real numbers, and
. What are the possible value(s) for
?
Solution 1
There are cases to consider:
Case :
of
,
, and
are positive and the other is negative. Without loss of generality (WLOG), we can assume that
and
are positive and
is negative. In this case, we have that
Case :
of
,
, and
are negative and the other is positive. WLOG, we can assume that
and
are negative and
is positive. In this case, we have that
Note these are the only valid cases, for neither negatives nor
positives would work as they cannot sum up to
. In both cases, we get that the given expression equals
.
Video Solution (CREATIVE THINKING + ANALYSIS!!!)
~Education, the Study of Everything
Video Solution by OmegaLearn
https://youtu.be/7an5wU9Q5hk?t=2362
Video Solutions
- Happytwin
~savannahsolver
https://www.youtube.com/watch?v=u6M6ECGok1o
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