Question

If x-1/x = 9 find the value of x +1/x

Answer 1

`√(85)`

Explanation:

Given

x -
`(1)/(x)` = 9 ← square both sides

(x -
`(1)/(x)`)² = 9²

x² - 2 +
`(1)/(x^2)` = 81 ( add 2 to both sides )

x² +
`(1)/(x^2)` = 83

Now

(x +
`(1)/(x)`)² = x² +
`(1)/(x^2)` + 2, thus

x² +
`(1)/(x^2)` = 83 + 2 = 85

(x +
`(1)/(x)` )²= 85 ( take the square root of both sides)

x +
`(1)/(x)` =
`√(85)`