A function [unparseable or potentially dangerous latex formula] is defined for all real numbers x. For all non-zero values x, we have
[unparseable or potentially dangerous latex formula]
Let [unparseable or potentially dangerous latex formula] denote the sum of all of the values of [unparseable or potentially dangerous latex formula] for which [unparseable or potentially dangerous latex formula] Compute the integer nearest to [unparseable or potentially dangerous latex formula]
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Mock AIME 3 #3 -Problem by Mildorf
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Mock AIME 3 #3 -Problem by Mildorf
by stupidityismygam » Wed Jul 11, 2007 4:14 pm
Last edited by stupidityismygam on Wed Jul 11, 2007 6:17 pm, edited 1 time in total.
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stupidityismygam - Ubiquitous Spammer
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by Roel » Wed Jul 11, 2007 5:38 pm
[unparseable or potentially dangerous latex formula]
Since we are told that [unparseable or potentially dangerous latex formula] we can substitute:
[unparseable or potentially dangerous latex formula].
By plugging in [unparseable or potentially dangerous latex formula] for [unparseable or potentially dangerous latex formula] into [unparseable or potentially dangerous latex formula] we get:
[unparseable or potentially dangerous latex formula]
Again we substitute [unparseable or potentially dangerous latex formula]:
[unparseable or potentially dangerous latex formula]
Substitute [unparseable or potentially dangerous latex formula]:
[unparseable or potentially dangerous latex formula].
Multiply by [unparseable or potentially dangerous latex formula] and setting it equal to [unparseable or potentially dangerous latex formula] we get:
[unparseable or potentially dangerous latex formula]
Sum of the roots is...[unparseable or potentially dangerous latex formula]
Since we are told that [unparseable or potentially dangerous latex formula] we can substitute:
[unparseable or potentially dangerous latex formula].
By plugging in [unparseable or potentially dangerous latex formula] for [unparseable or potentially dangerous latex formula] into [unparseable or potentially dangerous latex formula] we get:
[unparseable or potentially dangerous latex formula]
Again we substitute [unparseable or potentially dangerous latex formula]:
[unparseable or potentially dangerous latex formula]
Substitute [unparseable or potentially dangerous latex formula]:
[unparseable or potentially dangerous latex formula].
Multiply by [unparseable or potentially dangerous latex formula] and setting it equal to [unparseable or potentially dangerous latex formula] we get:
[unparseable or potentially dangerous latex formula]
Sum of the roots is...[unparseable or potentially dangerous latex formula]
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