Difference between revisions of "Mock AIME 1 Pre 2005 Problems/Problem 5"
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Revision as of 17:45, 21 March 2008
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |