If \(x = 7 - 4\sqrt 3 \) then the value of \(x + \frac{1}{x}\) is

Question

Question

This question was previously asked in

ISRO VSSC Technical Assistant Mechanical 9 June 2019 Official Paper

Answer 1

Explanation:

We have, \(x=7-4 \sqrt3\)

Placing this value of x in, \(x + \frac{1}{x}\) we get

\(x + \frac{1}{x}\) = \(7 - 4\sqrt 3 + \frac{1}{{7 - 4\sqrt 3 }}\)

Rationalizing the denominator of 2nd term

\(x + \frac{1}{x}\) = \(7 - 4\sqrt 3 \;+\;7 + 4\sqrt 3 \)

\(x + \frac{1}{x}\) = 14

Hence, the value of \(x + \frac{1}{x}\) for the given value of x is 14.