If α and β are the roots of the equation

$x^2 - 9x + 8 = 0$ (α > β) then find the value of

$α^2 - β^2$.

** Option:**

**A.**63

**B.**62

**C.**65

**D.**None

**Answer: C . 65**

** Justification:**

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