α and β are the roots of the  equation
$x^2 - 9x + 8 =0$
Here, a =1, b = -9 and c = 8
.`. α + β = ${-b}/a = {-(-9)}/1 = 9$
and
.`. αβ = ${c/a} = {8/1} = 8$
-> $α^2 + β^2 $
= $(α + β)^2 - 2αβ $
= $(9)^2 - 2(8)$
= 81 - 16
= 65