Fun With Quadratic Roots.....

Algebra Level 3

Let α\alpha and β\beta be the roots of the quadratic equation, x24x+5=0x^{2}-4x+5=0.

What is the value of,

α3+α4β2+α2β4+β3?\alpha^{3}+\alpha^{4}\beta^{2}+\alpha^{2}\beta^{4}+\beta^{3}?

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