Given (a2−1)x2−(a−1)x+a2−4a+3=0
For this to be an identity in x, the coefficients of various powers of x and constant term must be zero.
Put coefficient of x2=0,
⇒(a2−1)=0
⇒(a+1)(a−1)=0
⇒a=−1,1
Put coefficient of x=0,
⇒(a−1)=0
⇒a=1
Put constant term =0,
⇒a2−4a+3=0
⇒(a−1)(a−3)=0
⇒a=1,3
Hence, the common value of a is 1.
a=1