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

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

Answer»

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

Discussion

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