$\frac {1} {x ^ 3-1} + \frac {2} {x ^ 3-2} + \frac {3} {x ^ 3-3 } + \frac {4}{x ^ 3-4} = 2x ^ 4 - 5x - 4.$
Note: $x ^ 3 \neq1, 2, 3,$ and $4$. Determine the value of: $x ^ 6-5x ^ 3 = ?$
I think it would be more feasible to create a polynomial that has as roots the 4 terms $(\frac {1} {x ^ 3-1} ....)$ and use Girard
But arriving at $ y ^ 2 + 10y + 24 = x ^ 2 $ you can not do anything right?
answer: $\sqrt{2}-4$ or $-\sqrt{2}-4$