2004 AMC 10A Problems/Problem 4
Contents
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 .
Solution 2
We know that either or . The first equation simplifies to , which is false, so . Solving, we get .
See also
2004 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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All AMC 10 Problems and Solutions |
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