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If the system of equations ${(a + 2)}^{3} x + {(a + 7)}^{3} y + {(a + 15)}^{3} z = 0$ ; $(a + 2) x + (a + 7) y + (a + 15) z = 0; x + y + z = 0$ possess a non-trivial solution, then a =

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$- 8$

-1

answer is A.

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Detailed Solution

$|\begin{matrix} 1 & 1 & 1 \\ a + 2 & a + 7 & a + 15 \\ {(a + 2)}^{2} & {(a + 7)}^{3} & {(a + 15)}^{3} \end{matrix}| = 0 \Rightarrow 3 a + 24 = 0 \Rightarrow a = - 8$

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