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 ?

Question

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 ? (A) - 4 (B) 9 (C) - 9 (D) 4

Tardigrade Admin · Accepted Answer

|1&2&1 4&4&1 9&6&1||1&1&1 α&2α&3α α2&4α2&9α2| = -648 α ⇒ (-4) (2α3) = - 648 α ⇒ α2 = 81 ⇒ α = ±9

Q. Which of the following values of $α$ satisfy the equation.
$∣ ∣ (1 + α)^{2} (2 + α)^{2} (3 + α)^{2} (1 + 2 α)^{2} (2 + 2 α)^{2} (3 + 2 α)^{2} (1 + 3 α)^{2} (2 + 3 α)^{2} (3 + 3 α)^{2} ∣ ∣ = - 648 α ?$

- 4

9

- 9

4

$∣ ∣ 149246111 ∣ ∣ ∣ ∣ 1 α α^{2} 1 2 α 4 α^{2} 1 3 α 9 α^{2} ∣ ∣ = - 648 α$
$\Rightarrow (- 4) (2 α^{3}) = - 648 α$
$\Rightarrow α^{2} = 81$
$\Rightarrow α = \pm 9$

Q. Which of the following values of α satisfy the equation. ∣∣​(1+α)2(2+α)2(3+α)2​(1+2α)2(2+2α)2(3+2α)2​(1+3α)2(2+3α)2(3+3α)2​∣∣​=−648α?

- 4

9

- 9

4

∣∣​149​246​111​∣∣​∣∣​1αα2​12α4α2​13α9α2​∣∣​=−648α ⇒(−4)(2α3)=−648α ⇒α2=81 ⇒α=±9

Q. Which of the following values of $α$ satisfy the equation.
$∣ ∣ (1 + α)^{2} (2 + α)^{2} (3 + α)^{2} (1 + 2 α)^{2} (2 + 2 α)^{2} (3 + 2 α)^{2} (1 + 3 α)^{2} (2 + 3 α)^{2} (3 + 3 α)^{2} ∣ ∣ = - 648 α ?$

$∣ ∣ 149246111 ∣ ∣ ∣ ∣ 1 α α^{2} 1 2 α 4 α^{2} 1 3 α 9 α^{2} ∣ ∣ = - 648 α$
$\Rightarrow (- 4) (2 α^{3}) = - 648 α$
$\Rightarrow α^{2} = 81$
$\Rightarrow α = \pm 9$