Which of the following values of α satisfy the equation |(1+α)2(1+2α)2(1+3α)2(2+α)2(2+2α)2(2+3α)2(3+α)2(3+2α)2(3+3α)2|=−648α ?

C 2 − C 1 , C 3 − C 1 ⇒ − 8 α 3 = − 648 α ⇒ α = 0 , ± 9

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Which of the following values of $α$ satisfy the equation
$| \begin{matrix} {(1 + α)}^{2} & {(1 + 2 α)}^{2} & {(1 + 3 α)}^{2} \\ {(2 + α)}^{2} & {(2 + 2 α)}^{2} & {(2 + 3 α)}^{2} \\ {(3 + α)}^{2} & {(3 + 2 α)}^{2} & {(3 + 3 α)}^{2} \end{matrix} | = - 648 α ?$

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-9

answer is A, B, C.

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$C_{2} - C_{1}, C_{3} - C_{1} \Rightarrow - 8 α^{3} = - 648 α \Rightarrow α = 0, \pm 9$

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