Question

If \[x = 2 + \sqrt{3}\] ,  find the value of \[x + \frac{1}{x}\].

Answer 1

Given that, `x= 2+sqrt3` hence

\[\frac{1}{x}\]  is given as

. `1/x = 1/(2+sqrt3)`We are asked to find  `x +1/x `

We know that rationalization factor for `2+sqrt3` is`2-sqrt3` . We will multiply each side of the given expression  `1/(2+sqrt3)` by, `2-sqrt3` to get

. `1/x = 1/(2+sqrt3) xx(2-sqrt3)/(2-sqrt3)`

`= (2-sqrt3)/((2)^2-(sqrt3)^2)`

`= (2-sqrt3)/(4-3)`

`=2-sqrt3`

Therefore,

`x+1/x = 2+sqrt3 +2 - sqrt3`

`=4`

Hence value of the given expression is 4 .