2004 AMC 10A Problems/Problem 15
Contents
Problem
Given that and , what is the largest possible value of ?
Solution
Rewrite as .
We also know that because and are of opposite sign.
Therefore, is maximized when is minimized, which occurs when is the largest and is the smallest.
This occurs at , so .
Solution 2
If the answer choice is valid, then it must satisfy . We use answer choices from greatest to least since the question asks for the greatest value.
Answer choice . We see that if then
and . However, is not in the domain of , so is incorrect.
Answer choice , however, we can find a value that satisfies which simplifies to , such as .
Therefore, is the greatest.
See also
2004 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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