An algebra problem by Phudish Prateepamornkul

Algebra Level 3

\[ \begin{eqnarray} ax+by &=& 40 \\ ax^2+by^2 &=& 110 \\ ax^3+by^3 &=& 310 \\ ax^4+by^4 &=& 890 \end{eqnarray} \]

Let \(a,b,x,\) and \(y\) be real variables satisfying the system of equations above.

Find the value of \(ax^5+by^5 \).

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