If α and β are the roots of the equation x 2 + p x + 2 = 0 and 1 α and 1 β are the roots of the equation 2 x 2 + 2 q x + 1 = 0 , then α - 1 α β - 1 β α + 1 β β + 1 α is equal to :

Step-by-step solution

α ,   β are roots of x 2 + p x + 2 = 0 ⇒ α + β = - p ,   α β = 2 1 α , 1 β are roots of 2 x 2 + 2 q x + 1 = 0 ∴   α ,   β are roots of x 2 + 2 q x + 2 = 0 ⇒ α + β = - 2 q ,   α β = 2 ∴ p = 2 q     . . . ( i ) ⇒ α - 1 α β - 1 β α + 1 β β + 1 α = α β - α β - β α + 1 α β · α β + 1 α &#94