Question

If \[x + \sqrt{15} = 4,\] then \[x + \frac{1}{x}\] = 

Options

• 2

• 4

• 8

• 1

Answer 1

Given that .`x+sqrt15 = 4` It can be simplified as 

` x =4 -sqrt15`

`1/x = 1/(4-sqrt15)`

We need to find  `x+1/x`

We know that rationalization factor for `4-sqrt15  `is `4 +sqrt15`. We will multiply numerator and denominator of the given expression `1/(4-sqrt15)`by , `4+sqrt15` to get

`1/x = 1/(4-sqrt15) xx (4+sqrt15)/ (4+sqrt15) `

`= (4+sqrt15)/((4^2) - (sqrt15)^2)`

`= (4+sqrt15)/(16-15)`

`= 4+sqrt15`

Therefore,

`x +1/x = 4 - sqrt15 + 4 + sqrt15`

` = 4+ 4 `

 = ` 8 `