Difference between revisions of "2017 AMC 8 Problems/Problem 21"
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+ | ==Problem 21== | ||
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+ | Suppose <math>a</math>, <math>b</math>, and <math>c</math> are nonzero real numbers, and <math>a+b+c=0</math>. What are the possible value(s) for <math>\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|}</math>? | ||
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+ | <math>\textbf{(A) }0\qquad\textbf{(B) }1\text{ and }-1\qquad\textbf{(C) }2\text{ and }-2\qquad\textbf{(D) }0,2,\text{ and }-2\qquad\textbf{(E) }0,1,\text{ and }-1</math> | ||
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+ | ==Solution== | ||
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There are <math>2</math> cases to consider: | There are <math>2</math> cases to consider: | ||
Revision as of 13:34, 22 November 2017
Problem 21
Suppose ,
, and
are nonzero real numbers, and
. What are the possible value(s) for
?
Solution
There are cases to consider:
Case :
of
,
, and
are positive and the other is negative. WLOG 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 assume that
and
are negative and
is positive. In this case, we have that
In both cases, we get that the given expression equals .
~nukelauncher