Q83 / 180 · KCET 2017 · Mathematics

If \( \left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right| \) then \( x \) is equal to

  • A
    \( 2 \)
  • B
    \( 04 \)
  • C
    \( 08 \)
  • Correct answer
    D
    \( \pm 2 \sqrt{2} \)

Solution

Given that, \( \left|\begin{array}{cc}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right| \) \( 3-x^{2}=3-8 \) \( \Rightarrow x^{2}=8 \Rightarrow x=\pm 2 \sqrt{2} \)

Hence, the correct answer is option: 'D'.

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