# An algebra problem by Yeldo Pailo

Algebra Level 3

$$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$\lambda ({ x }^{ 2 }-x)+x+5=0$$. If $${ \lambda }_{ 1 }$$ and $${ \lambda }_{ 2 }$$ are the two values of $$\lambda$$ for which the roots $$\alpha$$ and $$\beta$$ are connected by the relation $$\frac { \alpha }{ \beta } +\frac { \beta }{ \alpha } =4$$, then find the value of $$\frac { { \lambda }_{ 1 } }{ { \lambda }_{ 2 } } +\frac { { { \lambda } }_{ 2 } }{ { \lambda }_{ 1 } }$$.

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