If α , β are the roots of the equation x 2 - 5 + 3 log 3 5 - 5 log 5 3 x + 3 3 log 3 5 1 3 - 5 log 5 3 2 3 - 1 = 0 then the equation, whose roots are α + 1 β and β + 1 α ,

Step-by-step solution

Given α , β are the roots of the equation x 2 - 5 + 3 log 3 5 - 5 log 5 3 x + 3 3 log 3 5 1 3 - 5 log 5 3 2 3 - 1 = 0 Now 3 log 3 5 - 5 log 5 3 = 3 log 3 5 - 3 log 3 5 log 5 3 = 3 log 3 5 - 3 log 3 5 = 0 Also 3 log 3 5 1 3 - 5 log 5 3 2 3 = 5 log 5 3 2 3 - 5 log 5 3 2 3 = 0 So, given equation becomes x 2 - 5 x - 3 = 0 i.e. α + β = 5 ;   α β = - 3 Now if the roots are α + 1 β and β + 1 α i.e., α β + 1 β & α β + 1 α i.e., - 2 &#9