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Author Topic: Maximize the Sum -- AIME #10  (Read 4872 times)

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Offline Ender

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Maximize the Sum -- AIME #10
« on: July 06, 2007, 10:08:29 pm »
Two positive integers differ by 60. The sum of their square roots is the square root of an integer that is not a perfect square. What is the maximum possible sum of the two integers?
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Offline rabbit

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Re: Maximize the Sum -- AIME #10
« Reply #1 on: July 07, 2007, 11:01:39 am »
Wait..the number's root isn't a perfect square, or the number isn't a perfect square?

Also, if you don't put a max, the answer is infinite.
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Offline Ender

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Re: Maximize the Sum -- AIME #10
« Reply #2 on: July 07, 2007, 04:18:43 pm »
As in,



where c is not a perfect square.

The answer is not infinite.

And anyways, this is the exact wording given on the AIME, although I must say sometimes I'm pissed off with their wording.
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Offline iago

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Re: Maximize the Sum -- AIME #10
« Reply #3 on: July 09, 2007, 01:11:00 pm »
I notice there's no hint/solution on your blog.. gonna post one?

<edit> is the answer 100?

a = 80
b = 20
« Last Edit: July 09, 2007, 01:37:02 pm by iago »
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Offline dark_drake

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Re: Maximize the Sum -- AIME #10
« Reply #4 on: July 09, 2007, 02:03:12 pm »
Is it 68?
4 and 64
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errr... something like that...

Offline Ender

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Re: Maximize the Sum -- AIME #10
« Reply #5 on: July 09, 2007, 06:36:05 pm »
Quote from: iago on July 09, 2007, 01:11:00 pm
I notice there's no hint/solution on your blog.. gonna post one?

<edit> is the answer 100?

a = 80
b = 20

I've just been too lazy/busy to post the solution I came up with ;o But fine, I'll do it now.

100 and 68 are incorrect.
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Offline Ender

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Re: Maximize the Sum -- AIME #10
« Reply #6 on: July 09, 2007, 08:09:40 pm »
K, blogged it.
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Offline dark_drake

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Re: Maximize the Sum -- AIME #10
« Reply #7 on: July 09, 2007, 08:19:48 pm »
Whoops, totally misread the problem.  :D
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errr... something like that...
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