Sunday, June 04, 2006


Verification needed, simple algebra

I am trying to do a simple calculation but there are enough variables that I am not sure if I got it all right.


k = 2x^2 + 2xy + y^2 - 2w^2 - z^2 - 2xz


x = (f_2 - f_1 - 2y - 4z)/2, w = (3f_1 - f_2 + 2y + 8z)/2


f_1 f_2 = T+k

I substitute for x and w into the first equation, and begin a tedious calculation where I want to do two completions of the square to isolate y on the left side, and get the following if I did it correctly:

9(2y + 10z + 5f_1 - f_2)^2 = (18z + 6f_1 - 2f_2)^2 - 18T - 54k + 45f_2^2 - 99f_1^2

I'm hoping I can have that equation verified.

If it's wrong, can someone give me the right one?

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