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The number of integral values of x satis...

The number of integral values of `x` satisfying `sqrt((-x^(2)+10x-16))ltx-2` is

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The correct Answer is:
3
`sqrt(-x^2+10x-16) lt x-2 `
We must have `-x^2+10 x -16 gt 0 `
or `x^2- 10 x+16 le 0 `
`rArr 2 le x le 8 `
Also `-x^2+10x- 16 lt x^2 -4x +4`
or `2x^2-14x+20 gt 0`
or `x^2- 7 x + 10 gt 0 `
`rArr x gt 5 or x lt 2`
From (1) and (2),`5 lt x le 8 rArr x = 6,7,8`
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