The solution of `|x+(1)/(x)| gt 2` is

Options

A. `R-{0}`
B. `R-{-1,0,1}`
C. `R-{1}`
D. `R-{-1,1}`

Answer

B

Explanation

`(b)` `|x+(1)/(x)|gt 2` (clearly `x ne 0`)
`implies|(x^(2)+1)/(x)| gt 2 implies (x^(2)+1)/(|x|) gt 2` (`:.x^(2)+1 gt 0`)
`impliesx^(2)+1 gt2|x|`
`implies|x|^(2)-2|x|+1 gt 0 implies (|x|-1)^(2) gt 0`
`implies |x| ne 1 implies x ne-1,1`
`:.xinR-{-1,0,1}`