Difference between revisions of "1950 AHSME Problems/Problem 38"
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==See Also== | ==See Also== |
Latest revision as of 00:35, 20 January 2024
Problem
If the expression has the value for all values of and , then the equation :
Solution
By , we have . Subtracting from both sides, giving . This factors to . Thus, , so the equation is .
Note: Alternatively, one may note that the equation is quadratic with a nonzero discriminant, so it will be satisfied for exactly two values of .
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 37 |
Followed by Problem 39 | |
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All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.