1981 AHSME Problems/Problem 28
Problem 28
Consider the set of all equations , where
,
,
are real constants and
for
. Let
be the largest positive real number which satisfies at least one of these equations. Let
be the largest positive real number that satisfies at least one of these equations. Which of the inequalities below does
satisfy?
Solution
Since and
will be as big as possible, we need
to be as big as possible, which means
is as small as possible. Since
is positive (according to the options), it makes sense for all of the coefficients to be
.
Evaluating gives a negative number,
1, and
a number greater than 1, so the answer is
See also
1981 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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