2004 AMC 10A Problems/Problem 15
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.
Solution 3
See also
2004 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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