Difference between revisions of "2017 AMC 8 Problems/Problem 21"
(→Video Solution) |
(→Video Solution) |
||
Line 17: | Line 17: | ||
==Video Solution== | ==Video Solution== | ||
https://youtu.be/FUEHirfk-tw | https://youtu.be/FUEHirfk-tw | ||
− | https://youtu.be/V9wCBTwvIZo | + | |
+ | https://youtu.be/V9wCBTwvIZo - Happytwin | ||
+ | |||
https://youtu.be/7an5wU9Q5hk?t=2362 | https://youtu.be/7an5wU9Q5hk?t=2362 | ||
Revision as of 22:24, 9 July 2021
Contents
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. 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. Without loss of generality, we can assume that
and
are negative and
is positive. In this case, we have that
In both cases, we get that the given expression equals .
Video Solution
https://youtu.be/V9wCBTwvIZo - Happytwin
https://youtu.be/7an5wU9Q5hk?t=2362
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.