Difference between revisions of "1984 AHSME Problems/Problem 20"
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Latest revision as of 11:51, 5 July 2013
Problem
The number of the distinct solutions to the equation
is
Solution
We can create a tree of possibilities, progressively eliminating the absolute value signs by creating different cases.
So we have possible solutions: and . Checking for extraneous solutions, we find that the only ones that work are and , so there are solutions, .
See Also
1984 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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