[Bleuachdu]

I came up with this equation a few months ago, and I have been playing around with it ever since. I've never really showed it to any other people, and I thought this would be a good way to evaluate it. This invlovles finding a an unknown square of a known number using two other variables. I came up with this for the purpose of finding a numbers square (x*x) without the use of a calculator. However, it has proven to be not all that useful. It still involves multiplying large numbers. The method used ends up being an identity (x^2=x^2), broken down into addition and multiplication. It shows a very interesting relationship between the root and square of two different numbers. Its very basic algebra, but I don't think I've seen anything like it before. If you have and I'm just an idiot, let me know! OK, the theory goes... Given any number in {R} X, the square can be calculated as the sum of y^2 + xz + yz, where Y is any number in {R} and Z is the difference of X and Y.

[quote:2a502]
EQUATION
{R,R}
x^2 = x squared
y^2 = y squared
z = x-y

x^2 = xz + yz + y^2

Substitute for Z
x^2 = [x(x-y) + y(x-y)] + y^2

x^2 = [x^2 -xy + xy - y^2] + y^2

x^2 = [x^2 - y^2] + y^2

x^2 = x^2

EXAMPLE
x = 34
y = 4
x^2 = ?
y^2 = 16
z = 30

x^2 = 34*30 + 4*30 + 16

x^2 = 1020 + 120 + 16

x^2 = 1156
[/quote:2a502]

Can anyone disprove it? If so, let me know. The Domain and Range may not be {R,R}, I'm not sure. Find any problems with it ? Like I said, I've never done much with it other than think about it and play around with it. Its not very practical or useful, but it is fairly interesting. Gimme some feedback!