If [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are numbers such that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula], then find [unparseable or potentially dangerous latex formula].
Hint: Don't solve for [unparseable or potentially dangerous latex formula]
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Mock AIME 5 #3 2007 -Problem by Altheman
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Mock AIME 5 #3 2007 -Problem by Altheman
by stupidityismygam » Tue Jul 03, 2007 10:46 pm
Last edited by stupidityismygam on Wed Jul 04, 2007 1:39 pm, edited 1 time in total.
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stupidityismygam - Ubiquitous Spammer
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by Quelloquialism » Wed Jul 04, 2007 12:20 pm
Equation 1: [unparseable or potentially dangerous latex formula]
Equation 2: [unparseable or potentially dangerous latex formula]
Start with equation 1.
[unparseable or potentially dangerous latex formula]
Cube both sides.
[unparseable or potentially dangerous latex formula]
Expand.
[unparseable or potentially dangerous latex formula]
Rearrange it.
[unparseable or potentially dangerous latex formula]
Factor.
[unparseable or potentially dangerous latex formula]
Substitute in equations 1 and 2.
[unparseable or potentially dangerous latex formula]
Subtract off 21.
[unparseable or potentially dangerous latex formula]
Divide by [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Rearrange it.
[unparseable or potentially dangerous latex formula]
Simplify.
[unparseable or potentially dangerous latex formula]
I hope that's right, anyway.
Equation 2: [unparseable or potentially dangerous latex formula]
Start with equation 1.
[unparseable or potentially dangerous latex formula]
Cube both sides.
[unparseable or potentially dangerous latex formula]
Expand.
[unparseable or potentially dangerous latex formula]
Rearrange it.
[unparseable or potentially dangerous latex formula]
Factor.
[unparseable or potentially dangerous latex formula]
Substitute in equations 1 and 2.
[unparseable or potentially dangerous latex formula]
Subtract off 21.
[unparseable or potentially dangerous latex formula]
Divide by [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Rearrange it.
[unparseable or potentially dangerous latex formula]
Simplify.
[unparseable or potentially dangerous latex formula]
I hope that's right, anyway.
- Quelloquialism
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by stupidityismygam » Wed Jul 04, 2007 1:38 pm
yep yep yep good job...that was a lot more efficient than my solution....i didn't take advantage of the xy=1 :(
Equation 1: [unparseable or potentially dangerous latex formula]
Equation 2: [unparseable or potentially dangerous latex formula]
Divide equation 1 by equation 2 to get Equation 3: [unparseable or potentially dangerous latex formula]
Square equation 3 (I could've cubed it...but i didn't think of it) to get Equation 4: [unparseable or potentially dangerous latex formula]
Multiply equation 3 by equation 4 to get [unparseable or potentially dangerous latex formula]
Then subtract over to get [unparseable or potentially dangerous latex formula]
Equation 1: [unparseable or potentially dangerous latex formula]
Equation 2: [unparseable or potentially dangerous latex formula]
Divide equation 1 by equation 2 to get Equation 3: [unparseable or potentially dangerous latex formula]
Square equation 3 (I could've cubed it...but i didn't think of it) to get Equation 4: [unparseable or potentially dangerous latex formula]
Multiply equation 3 by equation 4 to get [unparseable or potentially dangerous latex formula]
Then subtract over to get [unparseable or potentially dangerous latex formula]
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stupidityismygam - Ubiquitous Spammer
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