Which of the following values of α satisfy the equation 1 + α 2 1 + 2 α 2 1 + 3 α 2 2 + α 2 2 + 2 α 2 2 + 3 α 2 3 + α 2 3 + 2 α 2 3 + 3 α 2 = - 648 α ?

Step-by-step solution

1 + α 2 1 + 2 α 2 1 + 3 α 2 2 + α 2 2 + 2 α 2 2 + 3 α 2 3 + α 2 3 + 2 α 2 3 + 3 α 2 R 2 → R 2 - R 1 (Take common) R 3 → R 3 - R 1 2 1 + α 2 1 + 2 α 2 1 + 3 α 2 3 + 2 α 3 + 4 α 3 + 6 α 4 + 2 α 4 + 4 α 4 + 6 α R 3 → R 3 - R 2 2 1 + α 2 1 + 2 α 2 1 + 3 α 2 3 + 2 α 3 + 4 α 3 + 6 α 1 1 1 C 2 → C 2 - C 1 (Take common) C 3 → C 3 - C 1 ∴ 2 α 2 . α 1 + α 2 2 + 3 α 2 + 4 α 3 + 2 α 2 2 1 0 0 4 α 2 - 2 α = - 8 α 3 = - 648 α α = 0 , α 2 = 81 , α = ± 9