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?
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.
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.
I notice there's no hint/solution on your blog.. gonna post one?
<edit> is the answer 100?
a = 80
b = 20
Is it 68?
4 and 64
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.
K, blogged it.
Whoops, totally misread the problem. :D