Q54 / 170 · Manipal (MET) 2021 · Mathematics

If $x=\frac{2 \sqrt{2}-\sqrt{7}}{2 \sqrt{2}+\sqrt{7}}$, then $x+x^{-1}$ is equal to

  • A
    28
  • B
    32
  • Correct answer
    C
    30
  • D
    24

Solution

Given, $x=\frac{2 \sqrt{2}-\sqrt{7}}{2 \sqrt{2}+\sqrt{7}}$ $\begin{aligned} \therefore \quad x+\frac{1}{x} & =\frac{2 \sqrt{2}-\sqrt{7}}{2 \sqrt{2}+\sqrt{7}}+\frac{2 \sqrt{2}+\sqrt{7}}{2 \sqrt{2}-\sqrt{7}} \\ & =\frac{8+7-4 \sqrt{14}+8+7+4 \sqrt{14}}{8-7}=30\end{aligned}$

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

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