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.
Given
k = 2x^2 + 2xy + y^2 - 2w^2 - z^2 - 2xz
and
x = (f_2 - f_1 - 2y - 4z)/2, w = (3f_1 - f_2 + 2y + 8z)/2
and
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?
Given
k = 2x^2 + 2xy + y^2 - 2w^2 - z^2 - 2xz
and
x = (f_2 - f_1 - 2y - 4z)/2, w = (3f_1 - f_2 + 2y + 8z)/2
and
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?