I thought of three numbers.
Their sum is 6.
The sum of their squares is 8.
The sum of their cubes is 5.
What is the sum of their fourth powers?

(In reply to Imagine by Larry)

The point of the solution by np_rt is that it is not necessary to calculate each of the three numbers (a, b, c, d, e, f, in your notation) in order to calculate the sum of their fourth powers.  Indeed, it is much easier not to solve for the three numbers.

Posted by Nick Hobson on 2004-07-06 19:13:49