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TS EAMCET · Maths · Basic of Mathematics

If \(x=\frac{1}{2}\left(\sqrt{7}+\frac{1}{\sqrt{7}}\right)\), then \(\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}\) is equal to

  1. A \(1\)
  2. B \(2\)
  3. C \(3\)
  4. D \(4\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(3\)

Step-by-step Solution

Detailed explanation

Given that, \(\begin{aligned} x & =\frac{1}{2}\left(\sqrt{7}+\frac{1}{\sqrt{7}}\right) \\ \Rightarrow \quad x^2 & =\frac{1}{4}\left(7+\frac{1}{7}+2\right)=\frac{1}{4}\left(\frac{64}{7}\right) \\ & =\frac{16}{7} \end{aligned}\) Now,…