Question

α, β are roots of y² – 2y –7 = 0 find, 

α³ + β³ 

Answer 1

α, β are roots of y² – 2y –7 = 0  

\[a = 1, b = - 2, c = - 7\] 

\[\alpha^3 + \beta^3 = \left( \alpha + \beta \right)^3 - 3\alpha\beta\left( \alpha + \beta \right)\]
\[ = \left( 2 \right)^3 - 3\left( - 7 \right)\left( 2 \right)\]
\[ = 8 + 42\]
\[ = 50\]