An algebra problem by Phudish Prateepamornkul

Algebra Level 3

ax+by=40ax2+by2=110ax3+by3=310ax4+by4=890 \begin{aligned} ax+by &=& 40 \\ ax^2+by^2 &=& 110 \\ ax^3+by^3 &=& 310 \\ ax^4+by^4 &=& 890 \end{aligned}

Let a,b,x,a,b,x, and yy be real variables satisfying the system of equations above.

Find the value of ax5+by5ax^5+by^5 .

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