2004 AMC 10A Problems/Problem 4
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Problem
What is the value of 
if 
?
Solution
is the distance between and 
; 
is the distance between and 
.
Therefore, the given equation says is equidistant from and , so 
.
Alternatively, we can solve by casework (a method which should work for any similar problem involving absolute values of real numbers). If 
, then 
and 
, so we must solve 
, which has no solutions. Similarly, if 
, then 
and 
, so we must solve 
, which also has no solutions. Finally, if 
, then and , so we must solve 
, which has the unique solution 
.
See also
| 2004 AMC 10A (Problems • Resources) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 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 | ||
