2002 AMC 10B Problems/Problem 13
Contents
[hide]Problem
Find the value(s) of such that is true for all values of .
Solution
We have .
As must be true for all , we must have , hence .
Solution 2
Since we want only the -variable to be present, we move the terms only with the -variable to one side, thus constructing to . For there to be infinite solutions for and there is no , we simply find a value of such that the equation is symmetrical. Therefore,
There is only one solution, namely or
See Also
2002 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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All AMC 10 Problems and Solutions |
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