collinearity

Algebra Level 4

if α , β , γ , δ \alpha ,\beta ,\gamma ,\delta are distinct and different from 2 and the points ( α 4 α − 2 , α 3 − 5 α − 2 ) , ( β 4 β − 2 , β 3 − 5 β − 2 ) , ( γ 4 γ − 2 , γ 3 − 5 γ − 2 ) , ( δ 4 δ − 2 , δ 3 − 5 δ − 2 ) \left( \frac { { \alpha }^{ 4 } }{ \alpha -2 } ,\frac { { \alpha }^{ 3 }-5 }{ \alpha -2 } \right) ,\quad \left( \frac { { \beta }^{ 4 } }{ \beta -2 } ,\frac { { \beta }^{ 3 }-5 }{ \beta -2 } \right) ,\quad \left( \frac { { \gamma }^{ 4 } }{ \gamma -2 } ,\frac { { \gamma }^{ 3 }-5 }{ \gamma -2 } \right) ,\quad \left( \frac { { \delta }^{ 4 } }{ \delta -2 } ,\frac { { \delta }^{ 3 }-5 }{ \delta -2 } \right) are collinear

then α β γ δ \alpha \beta \gamma \delta =

αβγδ=3∑α+5∑αβ αβγδ=2∑αβγ+5∑α αβγδ=5∑α+3∑αβ αβγδ=5∑αβγ+2∑α

Huge Wolverine by huge wolverine , 24, India

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