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General Forums => Academic / School => Math and Other Problems => Topic started by: Ender on July 06, 2007, 10:08:29 PM

Title: Maximize the Sum -- AIME #10
Post by: Ender 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?
Title: Re: Maximize the Sum -- AIME #10
Post by: rabbit 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.
Title: Re: Maximize the Sum -- AIME #10
Post by: Ender on July 07, 2007, 04:18:43 PM
As in,

(http://latex.sidoh.org/?render=%5Csqrt%20a%20%2B%20%5Csqrt%20b%20%3D%20%5Csqrt%20c%20)

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.
Title: Re: Maximize the Sum -- AIME #10
Post by: 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
Title: Re: Maximize the Sum -- AIME #10
Post by: dark_drake on July 09, 2007, 02:03:12 PM
Is it 68?
4 and 64
Title: Re: Maximize the Sum -- AIME #10
Post by: Ender 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.
Title: Re: Maximize the Sum -- AIME #10
Post by: Ender on July 09, 2007, 08:09:40 PM
K, blogged it.
Title: Re: Maximize the Sum -- AIME #10
Post by: dark_drake on July 09, 2007, 08:19:48 PM
Whoops, totally misread the problem.  :D