Maximize the Sum -- AIME #10

[Ender]

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?

[rabbit]

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.

[Ender]

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.

[iago]

I notice there's no hint/solution on your blog.. gonna post one?

<edit> is the answer 100?

a = 80
b = 20

[dark_drake]

Is it 68?
4 and 64

[Ender]

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.

[Ender]

K, blogged it.

[dark_drake]

Whoops, totally misread the problem.  :D