# Polynomial system of 6 variables

1. Jul 19, 2015

### Bruno Tolentino

U = A a²
V = 2 A a b
W = A b²
u = 2 A a c + B a
v = 2 A b c + B b
w = A c² + B c + C

I'd like to solve this system for A, B, C, a, b, c. Is it possible!?

2. Jul 19, 2015

### Suraj M

If you want those terms, in terms of all the other terms, then i dont think you can, if in terms of U,V,W,u,v,w included then ofcourse, it would be simple,
the basic problem is you have only one equation with U in it, or were you trying to say $U$instead of $u$?

3. Jul 19, 2015

### DDH

Unless i'm mistaken, there are 12 variables and not 6 which means the system cannot be solved.

4. Jul 19, 2015

### Staff: Mentor

The system cannot be solved uniquely, which is different from saying that it can't be solved.

5. Jul 19, 2015

### DDH

I stand corrected.

6. Jul 19, 2015

### mathman

Assuming U,V,W,u,v,w are known, it might be possible. As a first step, the last three equations in A,B,C are linear, so you can get A,B,C, in terms of u,v,w,a,b,c. Substitute the expression for A into the first three equations. You now have polynomial expressions for a,b,c - good luck!

7. Jul 19, 2015