1.

Solution set of `(5x-1)lt (x+1)^(2)lt (7x -3)` isA. (1, 4)B. [2, 4]C. (2, 4)D. `(-oo, 1)cup(2, oo)`

Answer» Correct Answer - C
We have,
`(5x-1) lt (x+1)^(2) lt (7x-3)`
`rArr 5x-1 lt (x+1)^(2) " and " (x+1)^(2) lt (7x-3)`
`rArr (x+1)^(2)-(5x-1) gt 0 " and " (x+1)^(2) - (7x -3) lt 0`
`rArr x^(2) - 3x + 2 gt 0 " and " x^(2) - 5x + 4 lt 0`
`rArr (x-1)(x-2) gt o " and " (x-1) (x-4) lt 0`
`rArr x in (-oo, 1)cup(2, oo) " and " x in (1, 4)`
`rArr x in (2, 4)`


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