What is the best method for solving this summation equation?

[bj1]

Homework Statement

http://k1w1.no-ip.info/math.gif

Homework Equations

The Attempt at a Solution

A puzzle I'm trying to find a solution to, and have no idea on where to begin. Any pointers, or answers, appreciated. Thanks.

 

[HallsofIvy]

What exactly is the problem? You've given an equation but haven't said what problem you are trying to solve.

I also see many difficulties with the equation: you have a sum over j but there is no j in the numbers to be summed. If that is really what you mean then the result is just 5 times kx^ly^m for each l and m. But you also give different values of "k" for each l and m. Did you mean k_lm rather than just k? Looks to me like your equation becomes a 5 by 5 matrix equation with only some of the 25 entries involving x and y. Are we to assume that k_lm = 0 for combinations of l and m not in the table?

 

[bj1]

Hi HallsofIvy,

I'm trying to find the values of x & y. The equation is all that has been given, no other instructions or pointers. I'm rapidly learning that it doesn't appear to be 'standard' for want of a better term. Your assumptions could well be correct, and you may be onto the right path. Thanks.

 

[gabbagabbahey]

Your equation should really be written as

$$\sum_{j=0}^5 k_j x^{l_j}y^{m_j} =0$$

Since the values of $k$, $l$ and $m$ all depend on the value of $j$.

...as for the best method of solving this; give me a moment to think about it.