If x = 2 + √3, find the value of x + 1/x.

Question

If x = 2 + √3, find the value of \(x + \frac{1}{x}\).

Answer 1

Given: x = 2 + √3

\(\frac{1}{a} = \frac{1}{2+\sqrt3}\)

\(= \frac{1}{2+\sqrt3}\) x \(\frac{2-\sqrt3}{2-\sqrt3}\)

\(= \frac{(2-\sqrt3)}{((2)^2 - (\sqrt3)^2)}\)

\(= \frac{(2-\sqrt3)}{(4-3)}\)

\(= (2-\sqrt3)\)

Now,

\(x + \frac{1}{x}\) = (2 + √3) + (2 – √3)

= 2 + √3 + 2 – √3

= 4