The number of intergal values of x if `5x -1 lt (x+1)^2 lt 7 x-3 ` is

Options

A. `(1, 4)`
B. `[2, 4]`
C. `(2, 4)`
D. `(-oo, 1)uu(2, oo)`

Answer

C

Explanation

Solution set of `(5x - 1)` ………….
`(5x - 1) lt (x + 1)^(2) lt (7x - 3)`
`implies 5x - 1lt(x+1)^(2)lt(7x-3)`
`implies 5x-1lt(x+1)^(2) and (x+1)^(2)lt7x-3`
`implies (x+1)^(2)-5x+1gt0 and (x+1)^(2)- 7x+3 lt0`
`implies x^(2)-3x +2 gt 0 and x^(2) - 5x +4 lt 0`
`implies (x-1)(x-2)lt0 and (x-1)(x-4)lt0`
`implies x epsilon(-oo, 1)uu(2, oo) and 1 lt x lt 4`
`implies 2 lt x lt 4`