If α , β ≠ 0 , f n = α n + β n and 3 1 + f 1 1 + f 2 1 + f 1 1 + f 2 1 + f 3 1 + f 2 1 + f 3 1 + f 4 = K 1 - α 2 1 - β 2 α - β 2 , then K is equal to

Step-by-step solution

f 1 = α + β ,   f 2 = α 2 + β 2 ,   f 3 = α 3 + β 3 ,   f 4 = α 4 + β 4 So, the given determinant can be written as 1 + 1 + 1 1 + α + β 1 + α 2 + β 2 1 + α + β 1 + α 2 + β 2 1 + α 3 + β 3 1 + α 2 + β 2 1 + α 3 + β 3 1 + α 4 + β 4 = 1 1 1 1 α β 1 α 2 β 2 1 1 1 1 α α 2 1 β β 2 = 1 1 1 1 α β 1 α 2 β 2 1 1 1 1 α β 1 &