The sum of the coefficient of (αx2−2x+1)2019 is (α−1)2019⋅( On putring x=1) and similarly the sum of the coefficients of (x−αy)2019 is (1−α)2019 (on putting x=y=1 ) Now according to the question, (α−1)2019=(1−α)2019 ⇒α−1=1−α⇒α=1