Question

Find the number of integal values of x satisfying
`sqrt(-x^2+10x-16) lt x -2`

Answer 1

Correct Answer - 3
`sqrt(-x^(2)+10x-16) lt x-2`
We must have `-x^(2)+10x-16 ge0`
or `x^(2)-10x+16 le 0`
`implies 2 le x le 8 " (1)" `
Also `-x^(2)+10x-16 lt x^(2)-4x+4`
or `2x^(2)-14x+20 gt 0`
or `x^(2)-7x +10 gt 0`
` impliesx gt 5 " or " x lt 2 " (2)" `
From (1) and (2), `5lt x le 8 implies x=6,7,8`