Mock AIME 1 Pre 2005 Problems/Problem 5
Problem
Let and
be the two real values of
for which
The smaller of the two values can be expressed as
, where
and
are integers. Compute
.
Solution
Let . Then
and
. Factoring,
Solving gives us the quadratic
. The quadratic formula yields
, and
. Therefore,
.
See also
Mock AIME 1 Pre 2005 (Problems, Source) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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