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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Sequences and Series

NDA 2021 · Mathematics · Sequences and Series

If x^2, x,-8 are in AP, then which one of the following is correct?

If x2,x,−8x^2, x,-8 are in AP, then which one of the following is correct?

Options

  1. Ax∈{−2}x \in\{-2\}
  2. Bx∈{4}x \in\{4\}
  3. Cx∈{−2,4}x \in\{-2,4\}
  4. Dx∈{−4,2}x \in\{-4,2\}

Correct answer

C. x∈{−2,4}x \in\{-2,4\}

Step-by-step solution

x2,x,−8 are in A.P. ∴2x=x2−8⇒x2−2x+1−9=0\begin{aligned} & x^2, x,-8 \text{ are in A.P. } \\ & \therefore 2 x=x^2-8 \\ & \Rightarrow x^2-2 x+1-9=0\end{aligned}⇒(x−1)2=9∴(x−1)=±3∴x∈{−2,4}\begin{aligned} & \Rightarrow(x-1)^2=9 \\ & \therefore(x-1)= \pm 3 \\ & \therefore x \in\{-2,4\}\end{aligned}$
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