If α and β are the roots of the equation 1     5 1 3 - 4 7 2 7 19 - 3 19 4 19 1 19 4 1 3 - 4 7 2 x 2 - 5 x + 5 - 3 = - 4 , then the value of 2 - α 2 - β is

Step-by-step solution

Let, A = 1 - 4 3 7 then A - 1 = 7 19 - 3 19 4 19 1 19 Since, A A - 1 = I = A - 1 A Hence, 1 3 - 4 7 7 19 - 3 19 4 19 1 19 = I = 7 19 - 3 19 4 19 1 19 1 3 - 4 7 ⇒ 1 5 x 2 - 5 x + 5 - 3 = - 4 ⇒ x 2 + 5 x + 5 - 15 = - 4 ⇒ x 2 - 5 x - 6 = 0 ⇒ x = 6 , - 1 Hence, 2 - α 2 - β = - 4 × 3 = - 12