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If x2, x, -8 are in AP, then which one of the following is correct?
1. x ∈  {-2}
2. x ∈  {4}
3. x ∈  {-2, 4}
4. x ∈  {-4, 2}

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Correct Answer - Option 3 : x ∈  {-2, 4}

Concept:

Let us consider sequence a1, a2, a3 …. an is an A.P.

Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an-1

 

Calculation:

Since x2, x, -8 are in A.P we can write,

x - x2 = - 8 - x

⇒ x2 - 2x - 8 = 0

⇒ x2 - 4x + 2x - 8 = 0

⇒ x(x - 4) + 2(x - 4) = 0

⇒ (x - 4)(x + 2) = 0

⇒ x = -2, 4

∴ x ∈  {-2, 4}

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