The set of values of `x` satisfying `|(x^(2)-5x+4)/(x^(2)-4)| le 1` is

Options

A. `[0,(8)/(5)]`
B. `[(8)/(5),oo]`
C. `[-oo,-2]`
D. `R`

Answer

A

Explanation

`(a)` `|(x^(2)-5x+4)/(x^(2)-4)| le 1`
`implies -1 le (x^(2)-5x+4)/(x^(2)-4) le 1`
For `(x^(2)-5x+4)/(x^(2)-4) le 1`
`implies (x^(2)-5x+4)/(x^(2)-4)-1 le 0 implies (-5x+8)/(x^(2)-4) le 0`
`implies (5x-8)/((x-2)(x+2)) ge 0`

`implies xin(-2,8//5]uu(2,oo)` ..........`(i)`
Now `(x^(2)-5x+4)/(x^(2)-4)+1 ge 0 implies (x(2x-5))/((x-2)(x+2)) ge 0`

`implies x in (-oo,-2)uu[0,2)uu[5//2,oo)` .........`(ii)`
From `(i)` and `(ii)`, common values are `x in [0,8//5]uu[5//2,oo)`.