If α and β are the roots of the equation, 7 x 2 - 3 x - 2 = 0 , then the value of α 1 - α 2 + β 1 - β 2 is equal to:

Step-by-step solution

Given α and β are the roots of the equation, 7 x 2 - 3 x - 2 = 0 , then α + β = 3 7   ;   α β = - 2 7 Now α 1 - α 2 + β 1 - β 2 = ( α + β ) - α β ( α + β ) 1 - α 2 1 - β 2 = ( α + β ) - α β ( α + β ) 1 + ( α β ) 2 - α 2 + β 2 ⇒ ( α + β ) - α β ( α + β ) 1 + ( α β ) 2 - ( α + β ) 2 + 2 α β = 3 7 + 2 7 3