Let a , b , c , d be in arithmetic progression with common difference λ . If x + a - c x + b x + a x - 1 x + c x + b x - b + d x + d x + c = 2 , then value of λ 2 is equal to________.

Step-by-step solution

Since, a ,   b ,   c   &   d are in A . P . , therefore b - a = c - b = d - c = λ We have, x + a - c x + b x + a x - 1 x + c x + b x - b + d x + d x + c = 2 C 2 → C 2 - C 3 ⇒ x - 2 λ λ x + a x - 1 λ x + b x + 2 λ λ x + c = 2 R 2 → R 2 - R 1 ,    R 3 → R 3 - R 1 x - 2 λ λ x + a 2 λ - 1 0 b - a 4 λ 0 c - a = 2 ⇒ λ x - 2 λ 1 x + a 2 λ - 1 0 λ 4 λ 0 2 λ = 2 ⇒ - λ 4 &