1994 AHSME Problems/Problem 25
Problem
If and are non-zero real numbers such that then the integer nearest to is
Solution
We have two cases to consider: is positive or is negative. If is positive, we have and
Solving for in the top equation gives us . Plugging this in gives us: . Since we're told is not zero, we can divide by , giving us:
The discriminant of this is , which means the equation has no real solutions.
We conclude that is negative. In this case and . Negating the top equation gives us . We seek , so the answer is
-solution by jmania
See Also
1994 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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