Question for Havern

Well, this isnt really directed at Havern, so if anyone else can answer, that would be nice.

What is the trick for finding the sum of two adjacent squares?
ie.
33^2 + 34^2 = ?

Thanks

No clue. I seem to recall there being a specific trick for that, but it looked ugly, and strangely reminiscent of FOIL, so I didn't bother remembering it.

HTang wrote:No clue. I seem to recall there being a specific trick for that, but it looked ugly, and strangely reminiscent of FOIL, so I didn't bother remembering it.

The wierd part is, it appeared on a easy Dr. Numsen(????), so there must be an really easy trick for it. I'll try to beat it to death from now on o.O
2a^2 + 2a + 1 is what I derived where a is the first term, bu then again, this complicated of a trick wouldnt be on an easy numsen.

Ani wrote:

HTang wrote:No clue. I seem to recall there being a specific trick for that, but it looked ugly, and strangely reminiscent of FOIL, so I didn't bother remembering it.

The wierd part is, it appeared on a easy Dr. Numsen(????), so there must be an really easy trick for it. I'll try to beat it to death from now on o.O
2a^2 + 2a + 1 is what I derived where a is the first term, bu then again, this complicated of a trick wouldnt be on an easy numsen.

I found out the trick from Dulles. Since a^2 + b^2 = (a - b)^2 + 2ab and b = a + 1. You get:
a^2 + b^2 = (a - (a - 1))^2 + 2ab
and so
the trick is a^2 + b^2 = 2ab + 1 when b = a+1

Huh. That's kinda cool.